## Uhlmann, Gunther Alberto

Compute Distance To:
 Author ID: uhlmann.gunther-a Published as: Uhlmann, Gunther; Uhlmann, G.; Uhlmann, G. A.; Uhlmann, Gunther A.; Uhlmann, Günther Further Spellings: Uhlmann Arancibia, Gunther Alberto Homepage: http://sites.math.washington.edu/~gunther/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef
 Documents Indexed: 261 Publications since 1977 10 Contributions as Editor · 1 Further Contribution Biographic References: 1 Publication Co-Authors: 117 Co-Authors with 242 Joint Publications 2,624 Co-Co-Authors
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### Co-Authors

 26 single-authored 36 Stefanov, Plamen D. 24 Lassas, Matti J. 22 Wang, Jenn-Nan 19 Greenleaf, Allan 17 Salo, Mikko 15 de Hoop, Maarten V. 15 Vasy, András 14 Nakamura, Gen 10 Paternain, Gabriel Pedro 9 Krupchyk, Katya 8 Krupchyk, Katsiaryna 8 Kurylëv, Yaroslav Vadimovich 8 Sun, Ziqi 8 Sylvester, John Herbert 7 Liu, Hongyu 7 Wang, Yiran 7 Yamamoto, Masahiro 6 Bal, Guillaume 6 Imanuvilov, Oleg Yu. 6 Kenig, Carlos Eduardo 5 Pestov, Leonid 5 Zhai, Jian 5 Zhou, Hanming 4 Lai, Ru-Yu 4 Nagayasu, Sei 4 Oksanen, Lauri 4 Sjöstrand, Johannes 4 Smith, Hart F. 3 Bukhgeǐm, Alexandre L. 3 Caday, Peter 3 Chung, Tsz Shun Eric 3 Deng, Youjun 3 Dos Santos Ferreira, David 3 Finch, David V. 3 Guillarmou, Colin 3 Isozaki, Hiroshi 3 Katsnelson, Vitaly 3 Lin, Ching-Lung 3 Melrose, Richard Burt 3 Monard, François 3 Qian, Jianliang 3 Siltanen, Samuli 3 Zhao, Hongkai 2 Ammari, Habib M. 2 Dairbekov, Nurlan Slyamkhanovich 2 Dyatlov, Gleb V. 2 Feizmohammadi, Ali 2 Ghosh, Tuhin 2 Holman, Sean F. 2 Kang, Hyeonbae 2 Mendoza, Gerardo A. 2 Nolan, Clifford J. 2 Päivärinta, Lassi 2 Palacios, Benjamín 2 Sharafutdinov, Vladimir A. 2 Vogelius, Michael S. 2 Yang, Yang 2 Zou, Jun 1 Acosta, Sebastian 1 Albin, Pierre 1 Alessandrini, Giovanni 1 Andersson, Fredrik K. 1 Antoniano, José L. 1 Assylbekov, Yernat M. 1 Borcea, Liliana 1 Brown, Russell Murray 1 Brytik, Valeriy 1 Callias, Constantine J. 1 Cârstea, Cătălin Ion 1 Cheney, Margaret 1 Conca, Carlos 1 Covi, Giovanni 1 Croke, Christopher B. 1 Frigyik, Béla A. 1 Garnier, Josselin 1 Graham, C. Robin 1 Guillemin, Victor W. 1 Hamilton, Sarah Jane 1 Hansen, Sönke 1 Heck, Horst 1 Hintz, Peter 1 Ide, Takanori 1 Ilmavirta, Joonas 1 Isakov, Victor M. 1 Kettunen, Henrik 1 Kian, Yavar 1 Knudsen, Kim M. 1 Kow, Pu-Zhao 1 Kuchment, Peter A. 1 Lan, Ih-Ren 1 Lasiecka, Irena 1 Lee, John M. 1 Li, Jingzhi 1 Li, Qin 1 Li, Xiaosheng 1 Lie, Hongyu 1 Manasevich, Raul F. 1 Mönkkönen, Keijo 1 Muñoz, Claudio 1 Nachman, Adrian I. ...and 19 more Co-Authors
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### Serials

 23 Inverse Problems 18 Communications in Mathematical Physics 11 Communications in Partial Differential Equations 9 Communications on Pure and Applied Mathematics 9 Journal of Functional Analysis 8 Duke Mathematical Journal 8 SIAM Journal on Applied Mathematics 8 Inverse Problems and Imaging 7 SIAM Journal on Mathematical Analysis 6 American Journal of Mathematics 6 Transactions of the American Mathematical Society 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Mathematical Research Letters 5 Archive for Rational Mechanics and Analysis 5 Advances in Mathematics 5 Inventiones Mathematicae 5 Journal of Differential Geometry 5 Mathematische Annalen 5 Analysis & PDE 4 IMRN. International Mathematics Research Notices 4 Methods and Applications of Analysis 4 Annals of Mathematics. Second Series 3 Journal of the American Mathematical Society 3 Journal of Inverse and Ill-Posed Problems 3 Contemporary Mathematics 3 Mathematical Sciences Research Institute Publications 2 Annales de l’Institut Fourier 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Indiana University Mathematics Journal 2 Journal of Differential Equations 2 Proceedings of the American Mathematical Society 2 Advances in Applied Mathematics 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 The Journal of Geometric Analysis 2 Bulletin of the American Mathematical Society. New Series 2 Discrete and Continuous Dynamical Systems 2 SIAM Journal on Imaging Sciences 2 Journal of Spectral Theory 1 Acta Cientifica Venezolana 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Wave Motion 1 Journal of the Korean Mathematical Society 1 Mathematische Zeitschrift 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Chinese Annals of Mathematics. Series B 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 Geometric and Functional Analysis. GAFA 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Review 1 Communications in Analysis and Geometry 1 Applied and Computational Harmonic Analysis 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Electronic Journal of Differential Equations (EJDE) 1 Serdica Mathematical Journal 1 Electronic Research Announcements of the American Mathematical Society 1 The Journal of Fourier Analysis and Applications 1 Documenta Mathematica 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Annales Henri Poincaré 1 Multiscale Modeling & Simulation 1 The IMA Volumes in Mathematics and its Applications 1 Panoramas et Synthèses 1 Bulletin of Mathematical Sciences 1 East Asian Journal on Applied Mathematics 1 Séminaire Laurent Schwartz. EDP et Applications 1 Pure and Applied Analysis
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### Fields

 216 Partial differential equations (35-XX) 56 Differential geometry (53-XX) 52 Optics, electromagnetic theory (78-XX) 39 Global analysis, analysis on manifolds (58-XX) 28 Integral transforms, operational calculus (44-XX) 27 Mechanics of deformable solids (74-XX) 23 Numerical analysis (65-XX) 17 Biology and other natural sciences (92-XX) 15 Quantum theory (81-XX) 13 General and overarching topics; collections (00-XX) 10 Geophysics (86-XX) 8 Potential theory (31-XX) 8 Operator theory (47-XX) 7 Fluid mechanics (76-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Information and communication theory, circuits (94-XX) 4 Integral equations (45-XX) 3 Functional analysis (46-XX) 3 Relativity and gravitational theory (83-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Systems theory; control (93-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

245 Publications have been cited 5,043 times in 1,688 Documents Cited by Year
A global uniqueness theorem for an inverse boundary value problem. Zbl 0625.35078
Sylvester, John; Uhlmann, Gunther
1987
Electrical impedance tomography and Calderón’s problem. Zbl 1181.35339
Uhlmann, G.
2009
The Calderón problem with partial data. Zbl 1127.35079
Kenig, Carlos E.; Sjöstrand, Johannes; Uhlmann, Gunther
2007
Determining anisotropic real-analytic conductivities by boundary measurements. Zbl 0702.35036
Lee, John M.; Uhlmann, Gunther
1989
On nonuniqueness for Calderón’s inverse problem. Zbl 1054.35127
Greenleaf, Allan; Lassas, Matti; Uhlmann, Gunther
2003
Recovering a potential from partial Cauchy data. Zbl 0998.35063
Bukhgeim, Alexander L.; Uhlmann, Gunther
2002
Limiting Carleman weights and anisotropic inverse problems. Zbl 1181.35327
Dos Santos Ferreira, David; Kenig, Carlos E.; Salo, Mikko; Uhlmann, Gunther
2009
Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions. Zbl 0884.35167
Brown, Russell M.; Uhlmann, Gunther A.
1997
Two dimensional compact simple Riemannian manifolds are boundary distance rigid. Zbl 1076.53044
Pestov, Leonid; Uhlmann, Gunther
2005
Thermoacoustic tomography with variable sound speed. Zbl 1177.35256
Stefanov, Plamen; Uhlmann, Gunther
2009
An $$n$$-dimensional Borg-Levinson theorem. Zbl 0644.35095
Nachman, Adrian; Sylvester, John; Uhlmann, Gunther
1988
Cloaking devices, electromagnetic wormholes, and transformation optics. Zbl 1158.78004
Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2009
Boundary rigidity and stability for generic simple metrics. Zbl 1079.53061
Stefanov, Plamen; Uhlmann, Gunther
2005
Lagrangian intersection and the Cauchy problem. Zbl 0396.58006
Melrose, R. B.; Uhlmann, G. A.
1979
The inverse problem for the local geodesic ray transform. Zbl 1350.53098
Uhlmann, Gunther; Vasy, András
2016
On determining a Riemannian manifold from the Dirichlet-to-Neumann map. Zbl 0992.35120
Lassas, Matti; Uhlmann, Gunther
2001
Determining a magnetic Schrödinger operator from partial Cauchy data. Zbl 1148.35096
dos Santos Ferreira, David; Kenig, Carlos E.; Sjöstrand, Johannes; Uhlmann, Gunther
2007
The Calderón problem with partial data in two dimensions. Zbl 1201.35183
Imanuvilov, Oleg Yu.; Uhlmann, Gunther; Yamamoto, Masahiro
2010
Stability estimates for the $$X$$-ray transform of tensor fields and boundary rigidity. Zbl 1058.44003
Stefanov, Plamen; Uhlmann, Gunther
2004
Invisibility and inverse problems. Zbl 1159.35074
Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2009
Estimates for singular Radon transforms and pseudodifferential operators with singular symbols. Zbl 0717.44001
Greenleaf, Allan; Uhlmann, Gunther
1990
A uniqueness theorem for an inverse boundary value problem in electrical prospection. Zbl 0611.35088
Sylvester, John; Uhlmann, Gunther
1986
Nonlocal inversion formulas for the X-ray transform. Zbl 0668.44004
Greenleaf, Allan; Uhlmann, Gunther
1989
Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field. Zbl 0843.35134
Nakamura, Gen; Sun, Ziqi; Uhlmann, Gunther
1995
Inverse boundary value problems at the boundary-continuous dependence. Zbl 0632.35074
Sylvester, John; Uhlmann, Gunther
1988
Oscillatory integrals with singular symbols. Zbl 0462.58030
Guillemin, V.; Uhlmann, G.
1981
Full-wave invisibility of active devices at all frequencies. Zbl 1151.78006
Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2007
Inverse diffusion theory of photoacoustics. Zbl 1197.35311
Bal, Guillaume; Uhlmann, Gunther
2010
The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary. Zbl 1077.58012
Lassas, Matti; Taylor, Michael; Uhlmann, Gunther
2003
Inverse problems: seeing the unseen. Zbl 1325.35286
Uhlmann, Gunther
2014
The X-ray transform for a generic family of curves and weights. Zbl 1148.53055
Frigyik, Bela; Stefanov, Plamen; Uhlmann, Gunther
2008
Global uniqueness for an inverse boundary problem arising in elasticity. Zbl 0814.35147
Nakamura, Gen; Uhlmann, Gunther
1994
Tensor tomography on surfaces. Zbl 1275.53067
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2013
Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions. Zbl 1273.35308
Bal, Guillaume; Uhlmann, Gunther
2013
Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media. Zbl 0915.35066
Stefanov, Plamen; Uhlmann, Gunther
1998
On characterization of the range and inversion formulas for the geodesic X-ray transform. Zbl 1075.44003
Pestov, Leonid; Uhlmann, Gunther
2004
Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map. Zbl 1088.53027
Stefanov, Plamen; Uhlmann, Gunther
2005
Boundary rigidity with partial data. Zbl 1335.53055
Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
2016
Semiglobal boundary rigidity for Riemannian metrics. Zbl 1331.53066
Lassas, Matti; Sharafutdinov, Vladimir; Uhlmann, Gunther
2003
Complex geometrical optics solutions for Lipschitz conductivities. Zbl 1055.35144
Päivärinta, Lassi; Panchenko, Alexander; Uhlmann, Gunther
2003
Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations. Zbl 1396.35074
Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2018
Integral geometry of tensor fields on a class of non-simple Riemannian manifolds. Zbl 1151.53033
Stefanov, Plamen; Uhlmann, Gunther
2008
Inverse problems for the anisotropic Maxwell equations. Zbl 1226.35086
Kenig, Carlos E.; Salo, Mikko; Uhlmann, Gunther
2011
Inverse problems in quasilinear anisotropic media. Zbl 0886.35176
Sun, Ziqi; Uhlmann, Gunther
1997
The attenuated ray transform on simple surfaces. Zbl 1238.53058
Salo, Mikko; Uhlmann, Gunther
2011
Local Lens rigidity with incomplete data for a class of non-simple Riemannian manifolds. Zbl 1247.53049
Stefanov, Plamen; Uhlmann, Gunther
2009
Thermoacoustic tomography arising in brain imaging. Zbl 1220.35195
Stefanov, Plamen; Uhlmann, Gunther
2011
The boundary rigidity problem in the presence of a magnetic field. Zbl 1131.53047
Dairbekov, Nurlan S.; Paternain, Gabriel P.; Stefanov, Plamen; Uhlmann, Gunther
2007
Rigidity for metrics with the same lengths of geodesics. Zbl 0934.53031
Stefanov, Plamen; Uhlmann, Gunther
1998
An efficient Neumann series-based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed. Zbl 1279.94029
Qian, Jianliang; Stefanov, Plamen; Uhlmann, Gunther; Zhao, Hongkai
2011
Recovering singularities of a potential from singularities of scattering data. Zbl 0790.35112
Greenleaf, Allan; Uhlmann, Gunther
1993
The Calderón problem for the fractional Schrödinger equation. Zbl 1439.35530
Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther
2020
Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms. Zbl 0695.58026
Greenleaf, A.; Uhlmann, G.
1990
Recovery of a source term or a speed with one measurement and applications. Zbl 1302.35453
Stefanov, Plamen; Uhlmann, Gunther
2013
Tensor tomography: progress and challenges. Zbl 1303.92053
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2014
Identification of Lamé parameters by boundary measurements. Zbl 0803.35164
Nakamura, Gen; Uhlmann, Gunther
1993
Inverting the local geodesic X-ray transform on tensors. Zbl 07008552
Stefanov, Plamen; Uhlmann, Gunther; Vasy, András
2018
The Calderón problem for conormal potentials. I: Global uniqueness and reconstruction. Zbl 1061.35165
Greenleaf, Allan; Lassas, Matti; Uhlmann, Gunther
2003
Determining both sound speed and internal source in thermo- and photo-acoustic tomography. Zbl 1328.35316
Liu, Hongyu; Uhlmann, Gunther
2015
Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential. Zbl 1295.35366
Krupchyk, Katsiaryna; Uhlmann, Gunther
2014
The geodesic X-ray transform with fold caustics. Zbl 1271.53070
Stefanov, Plamen; Uhlmann, Gunther
2012
Generic uniqueness for an inverse boundary value problem. Zbl 0728.35132
Sun, Ziqi; Uhlmann, Gunther
1991
Inverse problems at the boundary for an elastic medium. Zbl 0840.35122
Nakamura, Gen; Uhlmann, Gunther
1995
Microlocal structure of involutive conical refraction. Zbl 0422.58026
Melrose, R. B.; Uhlmann, G. A.
1979
The attenuated ray transform for connections and Higgs fields. Zbl 1256.53021
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2012
An inverse source problem in optical molecular imaging. Zbl 1171.35126
Stefanov, Plamen; Uhlmann, Gunther
2008
Inverse problems for semilinear wave equations on Lorentzian manifolds. Zbl 1409.58019
Lassas, Matti; Uhlmann, Gunther; Wang, Yiran
2018
Inverse boundary value problems for the perturbed polyharmonic operator. Zbl 1317.35295
Krupchyk, Katsiaryna; Lassas, Matti; Uhlmann, Gunther
2014
Recovery of singularities for formally determined inverse problems. Zbl 0795.35142
Sun, Ziqi; Uhlmann, Gunther
1993
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions. Zbl 1328.53099
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2015
Is a curved flight path in SAR better than a straight one? Zbl 1291.35448
Stefanov, Plamen; Uhlmann, Gunther
2013
Quantitative thermo-acoustics and related problems. Zbl 1217.35207
Bal, Guillaume; Ren, Kui; Uhlmann, Gunther; Zhou, Ting
2011
Inverse problems with partial data in a slab. Zbl 1200.35331
Li, Xiaosheng; Uhlmann, Gunther
2010
Inverse boundary value problems and applications. Zbl 0787.35123
Uhlmann, Gunther
1992
Determining a first order perturbation of the biharmonic operator by partial boundary measurements. Zbl 1239.35184
Krupchyk, Katsiaryna; Lassas, Matti; Uhlmann, Gunther
2012
Reconstruction of the potential from partial Cauchy data for the Schrödinger equation. Zbl 1051.35103
Ammari, Habib; Uhlmann, Gunther
2004
Anisotropic inverse problems in two dimensions. Zbl 1054.35139
Sun, Ziqi; Uhlmann, Gunther
2003
Reconstructing discontinuities using complex geometrical optics solutions. Zbl 1146.35097
Uhlmann, Gunther; Wang, Jenn-Nan
2008
Boundary and lens rigidity, tensor tomography and analytic microlocal analysis. Zbl 1138.53039
Stefanov, Plamen; Uhlmann, Gunther
2007
Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain. Zbl 1238.35188
Krupchyk, Katsiaryna; Lassas, Matti; Uhlmann, Gunther
2012
Microlocal analysis of the X-ray transform with sources on a curve. Zbl 1086.35134
Finch, David; Lan, Ih-Ren; Uhlmann, Gunther
2003
Developments in inverse problems since Calderón’s foundational paper. Zbl 0963.35203
Uhlmann, Gunther
1999
Uniqueness and reconstruction for the fractional Calderón problem with a single measurement. Zbl 1452.35255
Ghosh, Tuhin; Rüland, Angkana; Salo, Mikko; Uhlmann, Gunther
2020
The geodesic X-ray transform with matrix weights. Zbl 1440.53083
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Günther; Zhou, Hanming
2019
A remark on partial data inverse problems for semilinear elliptic equations. Zbl 1431.35246
Krupchyk, Katya; Uhlmann, Gunther
2020
The geodesic ray transform on Riemannian surfaces with conjugate points. Zbl 1319.53086
Monard, François; Stefanov, Plamen; Uhlmann, Gunther
2015
Increasing stability in an inverse problem for the acoustic equation. Zbl 1302.65243
Nagayasu, Sei; Uhlmann, Gunther; Wang, Jenn-Nan
2013
Approximate quantum and acoustic cloaking. Zbl 1257.35156
Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2011
The Dirichlet to Neumann map and applications. Zbl 0713.35100
Sylvester, John; Uhlmann, Gunther
1990
Full and partial cloaking in electromagnetic scattering. Zbl 1359.35185
Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
2017
On deformation boundary rigidity and spectral rigidity of Riemannian surfaces with no focal points. Zbl 1065.53039
2000
Inverse backscattering for the acoustic equation. Zbl 0888.35129
Stefanov, Plamen; Uhlmann, Gunther
1997
Pseudo-differential operators with involutive double characteristics. Zbl 0389.35047
Uhlmann, Gunther
1977
Partial Cauchy data for general second order elliptic operators in two dimensions. Zbl 1260.35253
Imanuvilov, Oleg Yu.; Uhlmann, Gunther; Yamamoto, Masahiro
2012
Layer stripping for a transversely isotropic elastic medium. Zbl 0935.35176
Nakamura, Gen; Tanuma, Kazumi; Uhlmann, Gunther
1999
Propagation of polarization in elastodynamics with residual stress and travel times. Zbl 1232.74041
Hansen, Sönke; Uhlmann, Gunther
2003
An inverse boundary value problem for Maxwell’s equations. Zbl 0757.35091
Sun, Ziqi; Uhlmann, Gunther
1992
Optimal three-ball inequalities and quantitative uniqueness for the Stokes system. Zbl 1196.35165
Lin, Ching-Lung; Uhlmann, Gunther; Wang, Jenn-Nan
2010
Probling for electrical inclusions with complex spherical waves. Zbl 1142.35104
Ide, Takanori; Isozaki, Hiroshi; Nakata, Susumu; Siltanen, Samuli; Uhlmann, G.
2007
Optical tomography in two dimensions. Zbl 1084.45006
Stefanov, Plamen; Uhlmann, Gunther
2003
The higher order fractional Calderón problem for linear local operators: uniqueness. Zbl 07496414
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther
2022
Inverse boundary value problems for wave equations with quadratic nonlinearities. Zbl 07450446
Uhlmann, Gunther; Zhang, Yang
2022
Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge. Zbl 1482.53056
Stefanov, Plamen; Uhlmann, Gunther; Vasy, András
2021
Inverse problems for the fractional-Laplacian with lower order non-local perturbations. Zbl 1461.35223
Bhattacharyya, S.; Ghosh, T.; Uhlmann, G.
2021
Reconstruction of the collision kernel in the nonlinear Boltzmann equation. Zbl 1459.35400
Lai, Ru-Yu; Uhlmann, Gunther; Yang, Yang
2021
Reconstruction in the Calderón problem on conformally transversally anisotropic manifolds. Zbl 1478.35237
Feizmohammadi, Ali; Krupchyk, Katya; Oksanen, Lauri; Uhlmann, Gunther
2021
On an inverse boundary value problem for a nonlinear elastic wave equation. Zbl 1476.35338
Uhlmann, Gunther; Zhai, Jian
2021
Inverse problems for nonlinear hyperbolic equations. Zbl 1458.35486
Uhlmann, Gunther; Zhai, Jian
2021
Travel time tomography in stationary spacetimes. Zbl 1475.53084
Uhlmann, Gunther; Yang, Yang; Zhou, Hanming
2021
The Calderón problem for the fractional Schrödinger equation. Zbl 1439.35530
Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther
2020
Uniqueness and reconstruction for the fractional Calderón problem with a single measurement. Zbl 1452.35255
Ghosh, Tuhin; Rüland, Angkana; Salo, Mikko; Uhlmann, Gunther
2020
A remark on partial data inverse problems for semilinear elliptic equations. Zbl 1431.35246
Krupchyk, Katya; Uhlmann, Gunther
2020
Nonlinear interaction of waves in elastodynamics and an inverse problem. Zbl 1441.35262
de Hoop, Maarten; Uhlmann, Gunther; Wang, Yiran
2020
Determination of space-time structures from gravitational perturbations. Zbl 1450.83002
Uhlmann, Gunther; Wang, Yiran
2020
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities. Zbl 1459.35399
Krupchyk, Katya; Uhlmann, Gunther
2020
The Calderón problem for quasilinear elliptic equations. Zbl 1457.35093
Muñoz, Claudio; Uhlmann, Gunther
2020
The light ray transform on Lorentzian manifolds. Zbl 1452.44006
Lassas, Matti; Oksanen, Lauri; Stefanov, Plamen; Uhlmann, Gunther
2020
The geodesic X-ray transform with matrix weights. Zbl 1440.53083
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Günther; Zhou, Hanming
2019
On an inverse boundary problem arising in brain imaging. Zbl 1416.35254
Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
2019
Inverse problems for the stationary transport equation in the diffusion scaling. Zbl 1437.35707
Lai, Ru-Yu; Li, Qin; Uhlmann, Gunther
2019
Travel time tomography. Zbl 1421.53077
Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras; Zhou, Hanming
2019
Reconstruction of Lorentzian manifolds from boundary light observation sets. Zbl 1430.53022
Hintz, Peter; Uhlmann, Gunther
2019
Scattering control for the wave equation with unknown wave speed. Zbl 1412.35377
Caday, Peter; de Hoop, Maarten V.; Katsnelson, Vitaly; Uhlmann, Gunther
2019
Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit. Zbl 1428.35682
Krupchyk, Katya; Uhlmann, Gunther
2019
Reconstruction of piecewise smooth wave speeds using multiple scattering. Zbl 1426.35237
Caday, Peter; De Hoop, Maarten V.; Katsnelson, Vitaly; Uhlmann, Gunther
2019
Nonlinear responses from the interaction of two progressing waves at an interface. Zbl 1409.58018
de Hoop, Maarten; Uhlmann, Gunther; Wang, Yiran
2019
X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds. (Transformée en rayons X et rigidité du bord pour les variétés asymptotiquement hyperboliques.) Zbl 1453.35190
Graham, C. Robin; Guillarmou, Colin; Stefanov, Plamen; Uhlmann, Gunther
2019
Lens rigidity for a particle in a Yang-Mills field. Zbl 1415.53011
Paternain, Gabriel P.; Uhlmann, Gunther; Zhou, Hanming
2019
Inverting the local geodesic ray transform of higher rank tensors. Zbl 1427.35349
De Hoop, Maarten V.; Uhlmann, Gunther; Zhai, Jian
2019
Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations. Zbl 1396.35074
Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2018
Inverting the local geodesic X-ray transform on tensors. Zbl 07008552
Stefanov, Plamen; Uhlmann, Gunther; Vasy, András
2018
Inverse problems for semilinear wave equations on Lorentzian manifolds. Zbl 1409.58019
Lassas, Matti; Uhlmann, Gunther; Wang, Yiran
2018
Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries. Zbl 1396.58022
Krupchyk, Katya; Uhlmann, Gunther
2018
On the microlocal analysis of the geodesic X-ray transform with conjugate points. Zbl 1387.53100
Holman, Sean; Uhlmann, Gunther
2018
Local recovery of the compressional and shear speeds from the hyperbolic DN map. Zbl 06850137
Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
2018
On the inverse problem of finding cosmic strings and other topological defects. Zbl 1391.83144
Lassas, Matti; Oksanen, Lauri; Stefanov, Plamen; Uhlmann, Gunther
2018
Krupchyk, Katya; Uhlmann, Gunther
2018
Inversion formulas and range characterizations for the attenuated geodesic ray transform. Zbl 1393.35284
Assylbekov, Yernat M.; Monard, François; Uhlmann, Gunther
2018
Tensor tomography in periodic slabs. Zbl 1395.44007
Ilmavirta, Joonas; Uhlmann, Gunther
2018
Propagation and recovery of singularities in the inverse conductivity problem. Zbl 1388.35225
Greenleaf, Allan; Lassas, Matti; Santacesaria, Matteo; Siltanen, Samuli; Uhlmann, Gunther
2018
Quantitative analysis of metal artifacts in X-ray tomography. Zbl 1409.35236
Palacios, Benjamin; Uhlmann, Gunther; Wang, Yiran
2018
Superdimensional metamaterial resonators from sub-Riemannian geometry. Zbl 1396.35014
Greenleaf, Allan; Kettunen, Henrik; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2018
Full and partial cloaking in electromagnetic scattering. Zbl 1359.35185
Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
2017
On regularized full- and partial-cloaks in acoustic scattering. Zbl 1375.35518
Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
2017
Reducing streaking artifacts in quantitative susceptibility mapping. Zbl 1397.35346
Palacios, Benjamin; Uhlmann, Gunther; Wang, Yiran
2017
Absolute continuity of the periodic Schrödinger operator in transversal geometry. Zbl 1368.35080
Krupchyk, Katsiaryna; Uhlmann, Gunther
2017
An inverse problem from condensed matter physics. Zbl 06818097
Lai, Ru-Yu; Shankar, Ravi; Spirn, Daniel; Uhlmann, Gunther
2017
The inverse problem for the local geodesic ray transform. Zbl 1350.53098
Uhlmann, Gunther; Vasy, András
2016
Boundary rigidity with partial data. Zbl 1335.53055
Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
2016
The X-ray transform for connections in negative curvature. Zbl 1343.53078
Guillarmou, Colin; Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2016
The Calderón problem with partial data for conductivities with 3/2 derivatives. Zbl 1362.35335
Krupchyk, Katya; Uhlmann, Gunther
2016
On the stable recovery of a metric from the hyperbolic DN map with incomplete data. Zbl 1348.35329
Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
2016
Inverse boundary problems for polyharmonic operators with unbounded potentials. Zbl 1345.35139
Krupchyk, Katsiaryna; Uhlmann, Gunther
2016
Local analytic regularity in the linearized Calderón problem. Zbl 1342.35456
Sjöstrand, Johannes; Uhlmann, Gunther
2016
Determining both sound speed and internal source in thermo- and photo-acoustic tomography. Zbl 1328.35316
Liu, Hongyu; Uhlmann, Gunther
2015
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions. Zbl 1328.53099
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2015
The geodesic ray transform on Riemannian surfaces with conjugate points. Zbl 1319.53086
Monard, François; Stefanov, Plamen; Uhlmann, Gunther
2015
Diffraction from conormal singularities. (Diffraction par singularités conormales.) Zbl 1322.58025
De Hoop, Maarten; Uhlmann, Gunther; Vasy, András
2015
On the range of the attenuated ray transform for unitary connections. Zbl 1369.44003
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2015
Regularized transformation-optics cloaking for the Helmholtz equation: from partial cloak to full cloak. Zbl 1325.35209
Li, Jingzhi; Liu, Hongyu; Rondi, Luca; Uhlmann, Gunther
2015
The Neumann-to-Dirichlet map in two dimensions. Zbl 1321.35024
Imanuvilov, O. Yu.; Uhlmann, Gunther; Yamamoto, M.
2015
Inverse boundary value problem for the Stokes and the Navier-Stokes equations in the plane. Zbl 1309.35085
Lai, Ru-Yu; Uhlmann, Gunther; Wang, Jenn-Nan
2015
Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields. Zbl 1329.35344
Bal, Guillaume; Monard, François; Uhlmann, Gunther
2015
Regularized transformation-optics cloaking in acoustic and electromagnetic scattering. Zbl 1346.35191
Liu, Hongyu; Uhlmann, Gunther
2015
An inverse kinematic problem with internal sources. Zbl 1320.86006
Pestov, Leonid; Uhlmann, Gunther; Zhou, Hanming
2015
On $$L^p$$ resolvent estimates for elliptic operators on compact manifolds. Zbl 1327.58023
Krupchyk, Katsiaryna; Uhlmann, Gunther
2015
The point source inverse back-scattering problem. Zbl 1334.35433
Rakesh; Uhlmann, Gunther
2015
Wave phenomena. 2nd edition. Zbl 1331.94023
Lassas, Matti; Salo, Mikko; Uhlmann, Gunther
2015
Inverse problems: seeing the unseen. Zbl 1325.35286
Uhlmann, Gunther
2014
Tensor tomography: progress and challenges. Zbl 1303.92053
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2014
Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential. Zbl 1295.35366
Krupchyk, Katsiaryna; Uhlmann, Gunther
2014
Inverse boundary value problems for the perturbed polyharmonic operator. Zbl 1317.35295
Krupchyk, Katsiaryna; Lassas, Matti; Uhlmann, Gunther
2014
Spectral rigidity and invariant distributions on Anosov surfaces. Zbl 1304.37021
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2014
Uniqueness for the inverse backscattering problem for angularly controlled potentials. Zbl 1294.33016
Rakesh; Uhlmann, Gunther
2014
Increasing stability of the inverse boundary value problem for the Schrödinger equation. Zbl 1330.35531
Isakov, V.; Nagayasu, S.; Uhlmann, G.; Wang, J.-N.
2014
Photoacoustic and thermoacoustic tomography with an uncertain wave speed. Zbl 1402.35314
Oksanen, Lauri; Uhlmann, Gunther
2014
30 years of Calderón’s problem. Zbl 1331.35394
Uhlmann, Gunther
2014
Tensor tomography on surfaces. Zbl 1275.53067
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2013
Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions. Zbl 1273.35308
Bal, Guillaume; Uhlmann, Gunther
2013
Recovery of a source term or a speed with one measurement and applications. Zbl 1302.35453
Stefanov, Plamen; Uhlmann, Gunther
2013
Is a curved flight path in SAR better than a straight one? Zbl 1291.35448
Stefanov, Plamen; Uhlmann, Gunther
2013
Increasing stability in an inverse problem for the acoustic equation. Zbl 1302.65243
Nagayasu, Sei; Uhlmann, Gunther; Wang, Jenn-Nan
2013
Inverse boundary problems for systems in two dimensions. Zbl 1310.81052
Albin, Pierre; Guillarmou, Colin; Tzou, Leo; Uhlmann, Gunther
2013
Instability of the linearized problem in multiwave tomography of recovery both the source and the speed. Zbl 1292.35337
Stefanov, Plamen; Uhlmann, Gunther
2013
Multiscale discrete approximations of Fourier integral operators associated with canonical transformations and caustics. Zbl 1290.35360
de Hoop, Maarten V.; Uhlmann, Gunther; Vasy, András; Wendt, Herwig
2013
Inverse problems and applications. Inside out II. Zbl 1277.65002
2013
Multiwave methods via ultrasound. Zbl 1316.35302
Stefanov, Plamen; Uhlmann, Gunther
2013
The geodesic X-ray transform with fold caustics. Zbl 1271.53070
Stefanov, Plamen; Uhlmann, Gunther
2012
The attenuated ray transform for connections and Higgs fields. Zbl 1256.53021
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
2012
Determining a first order perturbation of the biharmonic operator by partial boundary measurements. Zbl 1239.35184
Krupchyk, Katsiaryna; Lassas, Matti; Uhlmann, Gunther
2012
Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain. Zbl 1238.35188
Krupchyk, Katsiaryna; Lassas, Matti; Uhlmann, Gunther
2012
Partial Cauchy data for general second order elliptic operators in two dimensions. Zbl 1260.35253
Imanuvilov, Oleg Yu.; Uhlmann, Gunther; Yamamoto, Masahiro
2012
Reconstructions for some coupled-physics inverse problems. Zbl 1252.65185
Bal, Guillaume; Uhlmann, Gunther
2012
On uniqueness of Lamé coefficients from partial Cauchy data in three dimensions. Zbl 1264.35281
Imanuvilov, Oleg Yu.; Uhlmann, Gunther; Yamamoto, Masahiro
2012
Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations with limited smoothness. Zbl 1252.35287
De Hoop, Maarten V.; Holman, Sean F.; Smith, Hart F.; Uhlmann, Gunther
2012
Inverse problems for the anisotropic Maxwell equations. Zbl 1226.35086
Kenig, Carlos E.; Salo, Mikko; Uhlmann, Gunther
2011
The attenuated ray transform on simple surfaces. Zbl 1238.53058
Salo, Mikko; Uhlmann, Gunther
2011
Thermoacoustic tomography arising in brain imaging. Zbl 1220.35195
Stefanov, Plamen; Uhlmann, Gunther
2011
An efficient Neumann series-based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed. Zbl 1279.94029
Qian, Jianliang; Stefanov, Plamen; Uhlmann, Gunther; Zhao, Hongkai
2011
Quantitative thermo-acoustics and related problems. Zbl 1217.35207
Bal, Guillaume; Ren, Kui; Uhlmann, Gunther; Zhou, Ting
2011
...and 145 more Documents
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### Cited by 1,504 Authors

 119 Uhlmann, Gunther Alberto 56 Lassas, Matti J. 42 Salo, Mikko 39 Liu, Hongyu 36 de Hoop, Maarten V. 34 Stefanov, Plamen D. 33 Oksanen, Lauri 28 Wang, Jenn-Nan 27 Kian, Yavar 24 Yamamoto, Masahiro 23 Bellassoued, Mourad 23 Nakamura, Gen 20 Kurylëv, Yaroslav Vadimovich 19 Hyvönen, Nuutti 18 Lai, Ru-Yu 18 Paternain, Gabriel Pedro 18 Tzou, Leo 17 Greenleaf, Allan 17 Ilmavirta, Joonas 17 Monard, François 17 Siltanen, Samuli 16 Bal, Guillaume 16 Krishnan, Venkateswaran P. 16 Yang, Yang 15 Ammari, Habib M. 15 Harrach, Bastian 15 Li, Jichun 15 Lin, Yi-Hsuan 15 Quinto, Eric Todd 14 Isakov, Victor M. 14 Li, Jingzhi 14 Päivärinta, Lassi 14 Soccorsi, Eric 14 Sun, Ziqi 13 Deng, Youjun 13 Guillarmou, Colin 13 Haltmeier, Markus 13 Imanuvilov, Oleg Yu. 13 Knudsen, Kim M. 13 Santacesaria, Matteo 13 Vasy, András 12 Alessandrini, Giovanni 12 Choulli, Mourad 12 Hu, Guanghui 12 Huang, Yunqing 12 Ramm, Alexander G. 11 Alberti, Giovanni S. 11 Assylbekov, Yernat M. 11 Caro, Pedro 11 Feizmohammadi, Ali 11 Isozaki, Hiroshi 11 Nguyen, Hoai-Minh 11 Novikov, Roman G. 11 Rüland, Angkana 11 Scherzer, Otmar 11 Wang, Yiran 10 Bao, Gang 10 Belishev, Mikhail Igorevitch 10 Li, Qin 10 Lin, Ching-Lung 10 Sini, Mourad 10 Yang, Wei 10 Zhai, Jian 9 Chung, Francis J. 9 Garde, Henrik 9 Krupchyk, Katsiaryna 9 Ren, Kui 9 Triki, Faouzi 9 Vogelius, Michael S. 9 Zhong, Yimin 9 Zhou, Hanming 8 Felea, Raluca 8 Guo, Yukun 8 Holman, Sean F. 8 Ivanov, Sergei Vladimirovich 8 Klibanov, Michael V. 8 Kuchment, Peter A. 8 Kunyansky, Leonid A. 8 Li, Peijun 8 Milton, Graeme Walter 8 Mishra, Rohit Kumar 8 Ruiz, Alberto 8 Serov, Valery S. 8 Tamasan, Alexandru 8 Vashisth, Manmohan 8 Zhou, Ting 7 Beretta, Elena 7 Cârstea, Cătălin Ion 7 Daudé, Thierry 7 Dos Santos Ferreira, David 7 Francini, Elisa 7 Guevara Vasquez, Fernando 7 Kamran, Niky 7 Kang, Hyeonbae 7 Nicoleau, François 7 Sá Barreto, Antônio 7 Seeger, Andreas 7 Staboulis, Stratos 7 Vessella, Sergio 7 Wang, Xianchao ...and 1,404 more Authors
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### Cited in 265 Serials

 124 Inverse Problems 104 Inverse Problems and Imaging 86 Communications in Partial Differential Equations 65 SIAM Journal on Mathematical Analysis 60 Journal of Differential Equations 42 Applicable Analysis 42 Communications in Mathematical Physics 40 Journal of Inverse and Ill-Posed Problems 39 Journal of Mathematical Analysis and Applications 38 SIAM Journal on Applied Mathematics 36 The Journal of Geometric Analysis 35 Journal of Functional Analysis 34 SIAM Journal on Imaging Sciences 30 Journal de Mathématiques Pures et Appliquées. Neuvième Série 26 Journal of Computational Physics 25 Transactions of the American Mathematical Society 24 Archive for Rational Mechanics and Analysis 24 Inverse Problems in Science and Engineering 23 Proceedings of the American Mathematical Society 20 Journal of Mathematical Physics 19 Duke Mathematical Journal 17 Mathematische Annalen 16 Advances in Mathematics 16 The Journal of Fourier Analysis and Applications 16 Journal of Spectral Theory 15 Annales de l’Institut Fourier 14 Wave Motion 13 Journal of Computational and Applied Mathematics 13 Annales Henri Poincaré 11 Computers & Mathematics with Applications 11 Mathematical Methods in the Applied Sciences 10 Inventiones Mathematicae 9 Communications on Pure and Applied Mathematics 9 Applied Mathematics Letters 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Journal of the American Mathematical Society 8 SIAM Journal on Scientific Computing 8 Calculus of Variations and Partial Differential Equations 7 Numerische Mathematik 7 Advances in Applied Mathematics 7 European Journal of Applied Mathematics 7 Discrete and Continuous Dynamical Systems 7 Multiscale Modeling & Simulation 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Applied Mathematics and Computation 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Revista Matemática Iberoamericana 6 Applied and Computational Harmonic Analysis 6 Journal of Mathematical Sciences (New York) 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Journal of Pseudo-Differential Operators and Applications 6 Mathematical Control and Related Fields 6 Electronic Research Archive 5 Journal d’Analyse Mathématique 5 Arkiv för Matematik 5 Mathematics of Computation 5 Journal of Geometry and Physics 5 Mathematische Zeitschrift 5 Numerical Functional Analysis and Optimization 5 SIAM Journal on Numerical Analysis 5 Acta Mathematicae Applicatae Sinica. English Series 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Bulletin of the American Mathematical Society. New Series 5 Engineering Analysis with Boundary Elements 5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 5 Journal of the European Mathematical Society (JEMS) 5 Complex Variables and Elliptic Equations 5 Analysis & PDE 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 SIAM Journal on Control and Optimization 4 Ergodic Theory and Dynamical Systems 4 Mathematical and Computer Modelling 4 Journal of Elasticity 4 Journal of Mathematical Imaging and Vision 4 Annals of Mathematics. Second Series 4 Journal of High Energy Physics 4 Journal of the Institute of Mathematics of Jussieu 4 Sibirskie Èlektronnye Matematicheskie Izvestiya 4 Communications in Computational Physics 3 Computer Methods in Applied Mechanics and Engineering 3 Nonlinearity 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Geometriae Dedicata 3 Mathematische Nachrichten 3 Siberian Mathematical Journal 3 Computational Mechanics 3 Geometric and Functional Analysis. GAFA 3 Bulletin des Sciences Mathématiques 3 Advances in Computational Mathematics 3 Doklady Mathematics 3 New Journal of Physics 3 Acta Mathematica Sinica. English Series 3 Foundations of Computational Mathematics 3 Journal of Applied Mathematics 3 Mathematical Modelling of Natural Phenomena 3 Advances in Applied Mathematics and Mechanics 3 Bulletin of Mathematical Sciences ...and 165 more Serials
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### Cited in 53 Fields

 1,308 Partial differential equations (35-XX) 326 Numerical analysis (65-XX) 285 Optics, electromagnetic theory (78-XX) 198 Global analysis, analysis on manifolds (58-XX) 156 Differential geometry (53-XX) 141 Biology and other natural sciences (92-XX) 133 Mechanics of deformable solids (74-XX) 132 Integral transforms, operational calculus (44-XX) 94 Quantum theory (81-XX) 91 Fluid mechanics (76-XX) 89 Operator theory (47-XX) 57 Information and communication theory, circuits (94-XX) 56 Harmonic analysis on Euclidean spaces (42-XX) 46 Calculus of variations and optimal control; optimization (49-XX) 41 Functional analysis (46-XX) 39 Potential theory (31-XX) 38 Integral equations (45-XX) 38 Geophysics (86-XX) 35 Dynamical systems and ergodic theory (37-XX) 34 Systems theory; control (93-XX) 30 Ordinary differential equations (34-XX) 27 Functions of a complex variable (30-XX) 18 Computer science (68-XX) 15 Statistical mechanics, structure of matter (82-XX) 13 Statistics (62-XX) 12 Probability theory and stochastic processes (60-XX) 12 Relativity and gravitational theory (83-XX) 11 Classical thermodynamics, heat transfer (80-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Real functions (26-XX) 9 Combinatorics (05-XX) 9 Approximations and expansions (41-XX) 8 Manifolds and cell complexes (57-XX) 7 Abstract harmonic analysis (43-XX) 6 Mechanics of particles and systems (70-XX) 5 General and overarching topics; collections (00-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Astronomy and astrophysics (85-XX) 5 Operations research, mathematical programming (90-XX) 4 Topological groups, Lie groups (22-XX) 4 Special functions (33-XX) 4 Difference and functional equations (39-XX) 3 Nonassociative rings and algebras (17-XX) 3 Geometry (51-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Convex and discrete geometry (52-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 General topology (54-XX)

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