## Borisov, Denis Ivanovich

Compute Distance To:
 Author ID: borisov.denis-i Published as: Borisov, D. I.; Borisov, Denis; Borisov, Denis I.; Borisov, D.; Borisov, Denis Ivanovich more...less Homepage: http://borisovdi.narod.ru/ External Links: MGP · ORCID · Math-Net.Ru · dblp
 Documents Indexed: 112 Publications since 1999 Reviewing Activity: 43 Reviews Co-Authors: 36 Co-Authors with 73 Joint Publications 776 Co-Co-Authors
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### Co-Authors

 37 single-authored 13 Cardone, Giuseppe 11 Veselić, Ivan 7 Freitas, Pedro 7 Gadyl’shin, Rustem R. 7 Znojil, Miloslav 6 Exner, Pavel 5 Mukhametrakhimova, A. I. 4 Bunoiu, Renata 4 Golovina, Anastasiya Mihajlovna 4 Konyrkulzhaeva, Maral Nurlanovna 3 Dmitriev, Sergey V. 3 Krejčiřík, David 3 Pankrashkin, Konstantin 3 Tautenhahn, Martin 3 Zezyulin, Dmitry A. 2 Durante, Tiziana 2 Hoecker-Escuti, Francisco 2 Kevrekidis, Panayotis G. 2 Saadatmand, Danial 2 Täufer, Matthias 1 Bikmetov, Aĭdar Renatovich 1 Chechkin, Gregory Aleksandrovich 1 Ekholm, Tomas 1 Faella, Luisa 1 Fatykhov, Minnekhan A. 1 Gaydukov, R. K. 1 Golovina, Anastasia 1 Javidan, Kurosh 1 Koroleva, Yu. O. 1 Kovařík, Hynek 1 Nakić, Ivica 1 Perugia, Carmen 1 Rose, Christian 1 Ružička, František 1 Sharapov, Timur Farkhatovich 1 Sultanov, Oskar A. 1 Zhou, Kun
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### Serials

 16 Journal of Mathematical Sciences (New York) 6 Journal of Mathematical Physics 6 Doklady Mathematics 5 Theoretical and Mathematical Physics 5 Sbornik: Mathematics 5 Annales Henri Poincaré 4 Mathematical Notes 3 Journal of Differential Equations 3 Journal of Functional Analysis 3 Russian Journal of Mathematical Physics 3 Izvestiya: Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Proceedings of the Steklov Institute of Mathematics 3 Journal of Physics A: Mathematical and Theoretical 3 Ufimskiĭ Matematicheskiĭ Zhurnal 2 Journal of Mathematical Analysis and Applications 2 Journal of Statistical Physics 2 Studies in Applied Mathematics 2 Asymptotic Analysis 2 Annals of Physics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Communications in Nonlinear Science and Numerical Simulation 2 Communications in Contemporary Mathematics 1 International Journal of Theoretical Physics 1 Nuclear Physics. B 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Advances in Mathematics 1 Functional Analysis and its Applications 1 Integral Equations and Operator Theory 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Zeitschrift für Analysis und ihre Anwendungen 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Communications in Analysis and Geometry 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Problemy Matematicheskogo Analiza 1 Mathematical Physics, Analysis and Geometry 1 Visnyk Kharkivs’kogo Universytetu. Seriya Matematyka, Prykladna Matematyka i Mekhanika 1 Differential Equations 1 Analysis & PDE
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### Fields

 73 Partial differential equations (35-XX) 38 Quantum theory (81-XX) 33 Operator theory (47-XX) 18 Ordinary differential equations (34-XX) 13 Statistical mechanics, structure of matter (82-XX) 5 Probability theory and stochastic processes (60-XX) 4 Optics, electromagnetic theory (78-XX) 3 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Approximations and expansions (41-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX)

### Citations contained in zbMATH Open

83 Publications have been cited 641 times in 273 Documents Cited by Year
Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in $$\mathbb R^d$$. Zbl 1180.35397
Borisov, Denis; Freitas, Pedro
2010
Discrete spectrum of an asymmetric pair of waveguides coupled through a window. Zbl 1156.35066
Borisov, D. I.
2006
Bound states in weakly deformed strips and layers. Zbl 1043.35046
Borisov, D.; Exner, P.; Gadyl’shin, R.; Krejčiřík, D.
2001
Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Zbl 1168.35401
Borisov, Denis; Freitas, Pedro
2009
Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094
Borisov, D.; Exner, P.; Gadyl’shin, R.
2002
Homogenization of the planar waveguide with frequently alternating boundary conditions. Zbl 1178.81088
Borisov, D.; Cardone, G.
2009
Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. Zbl 1361.35021
Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana
2016
$$\mathcal {PT}$$-symmetric waveguides. Zbl 1178.35141
Borisov, Denis; Krejčiřík, David
2008
On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Zbl 1210.82077
Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe
2010
Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics. Zbl 1282.35033
Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe
2013
Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008
Borisov, D.; Exner, P.
2004
Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. Zbl 1269.81050
Borisov, Denis; Pankrashkin, Konstantin
2013
Gap opening and split band edges in waveguides coupled by a periodic system of small windows. Zbl 1288.81046
Borisov, D. I.; Pankrashkin, K. V.
2013
Uniform resolvent convergence for strip with fast oscillating boundary. Zbl 1286.35025
Borisov, Denis; Cardone, Giuseppe; Faella, Luisa; Perugia, Carmen
2013
On the spectrum of a periodic operator with a small localized perturbation. Zbl 1169.34056
Borisov, D. I.; Gadyl’shin, R. R.
2008
On a model boundary value problem for Laplacian with frequently alternating type of boundary condition. Zbl 1137.35308
Borisov, Denis I.
2003
Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. Zbl 1185.35155
Borisov, Denis
2007
Distant perturbations of the Laplacian in a multi-dimensional space. Zbl 1143.35075
Borisov, Denis I.
2007
Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Zbl 1181.35151
Borisov, Denis; Freitas, Pedro
2009
Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. Zbl 1290.81038
Borisov, D.; Bunoiu, R.; Cardone, G.
2011
Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions. Zbl 1077.81038
Borisov, Denis; Ekholm, Tomas; Kovařík, Hynek
2005
Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043
Borisov, D.; Exner, P.
2006
Planar waveguide with ”twisted” boundary conditions: Discrete spectrum. Zbl 1273.81100
Borisov, Denis; Cardone, Giuseppe
2011
On the spectrum of a two-dimensional periodic operator with a small localized perturbation. Zbl 1233.35066
Borisov, D. I.
2011
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods. Zbl 1223.35248
Borisov, Denis; Cardone, Giuseppe
2011
On a waveguide with an infinite number of small windows. (Sur un guide d’onde avec un nombre infini de petites fentes.) Zbl 1211.35098
Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe
2011
The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Zbl 1241.47042
Borisov, Denis; Krejčiřík, David
2012
The spectrum of two quantum layers coupled by a window. Zbl 1115.81024
Borisov, D.
2007
Asymptotics and estimates for the eigenelements of the Laplacian with frequent nonperiod change of boundary conditions. Zbl 1067.35055
Borisov, D. I.
2003
Low lying eigenvalues of randomly curved quantum waveguides. Zbl 1292.81051
Borisov, Denis; Veselić, Ivan
2013
The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes. Zbl 1403.35023
Borisov, D. I.; Mukhametrakhimova, A. I.
2018
Low lying spectrum of weak-disorder quantum waveguides. Zbl 1208.82089
Borisov, Denis; Veselić, Ivan
2011
Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Zbl 1206.35029
Borisov, D.
2009
On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows. Zbl 1319.35134
Borisov, D. I.
2015
Some singular perturbations of periodic operators. Zbl 1147.34060
Borisov, D. I.
2007
Planar waveguide with “twisted” boundary conditions: small width. Zbl 1274.81108
Borisov, Denis; Cardone, Giuseppe
2012
Tunneling resonances in systems without a classical trapping. Zbl 1280.81035
Borisov, D.; Exner, P.; Golovina, A.
2013
The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Zbl 1177.34107
Borisov, D. I.; Gadyl’shin, R. R.
2006
Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. Zbl 1381.35027
Borisov, Denis; Tautenhahn, Martin; Veselić, Ivan
2017
On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation. Zbl 1364.35305
Borisov, D. I.; Dmitriev, S. V.
2017
On the extrema of band functions in periodic waveguides. Zbl 1308.34111
Borisov, D. I.; Pankrashkin, K. V.
2013
Asymptotics for the expected lifetime of Brownian motion on thin domains in $$\mathbb R^n$$. Zbl 1296.60220
Borisov, Denis; Freitas, Pedro
2013
The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis. Zbl 1137.34039
Borisov, D. I.; Gadyl’shin, R. R.
2007
Two-parameter asymptotics in a boundary value problem for the Laplacian. Zbl 1140.35544
Borisov, D. I.
2001
On eigenvalues of a $$\mathcal{PT}$$-symmetric operator in a thin layer. Zbl 1371.35178
Borisov, Denis I.; Znojil, Miloslav
2017
Multiply degenerate exceptional points and quantum phase transitions. Zbl 1329.81037
Borisov, Denis I.; Ružička, František; Znojil, Miloslav
2015
Two patterns of $$\mathcal{PT}$$-symmetry breakdown in a non-numerical six-state simulation. Zbl 1390.81172
Znojil, Miloslav; Borisov, Denis I.
2018
Boundary-value problem in a cylinder with frequently changing type of boundary conditions. Zbl 1045.35047
Borisov, D. I.
2002
Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Zbl 1304.35058
Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana
2014
Existence of the stationary solution of a Rayleigh-type equation. Zbl 1408.35118
Borisov, D. I.; Gaydukov, R. K.
2016
On the spectrum of the Laplacian with frequently alternating boundary conditions. Zbl 0945.35066
Borisov, D. I.; Gadyl’shin, R. R.
1999
Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. Zbl 1427.81028
Borisov, D. I.; Zezyulin, D. A.
2020
Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate. Zbl 1348.82039
Borisov, Denis; Golovina, Anastasia; Veselić, Ivan
2016
On a $$\mathcal{PT}$$-symmetric waveguide with a pair of small holes. Zbl 1321.47166
Borisov, D. I.
2013
Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip. Zbl 1405.35020
Borisov, D. I.
2018
Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. Zbl 1426.34039
Borisov, D. I.; Konyrkulzhaeva, M. N.
2019
Expansion of the spectrum in the weak disorder regime for random operators in continuum space. Zbl 1386.35291
Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan
2018
On a model graph with a loop and small edges. Holomorphy property of resolvent. Zbl 1458.34059
Borisov, D. I.; Mukhametrakhimova, A. I.
2020
On a Laplacian with frequently nonperiodically alternating boundary conditions. Zbl 1197.35027
Borisov, D. I.
2002
On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Zbl 1210.34071
Borisov, D. I.
2006
On the spectrum of deformations of compact double-sided flat hypersurfaces. Zbl 1282.35261
Borisov, Denis; Freitas, Pedro
2013
Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions. Zbl 1108.35032
Borisov, D. I.
2004
Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction. Zbl 1430.35169
Borisov, D. I.
2019
Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. Zbl 1339.81037
Borisov, D.; Tautenhahn, M.; Veselić, I.
2015
Multiscale unique continuation properties of eigenfunctions. Zbl 1337.35031
Borisov, Denis; Nakić, Ivica; Rose, Christian; Tautenhahn, Martin; Veselić, Ivan
2015
Expansion of the almost sure spectrum in the weak disorder regime. Zbl 1331.82026
Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan
2016
On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential. Zbl 1134.34337
Borisov, D. I.
2006
On a singularly perturbed boundary value problem for the Laplacian in a cylinder. Zbl 1274.35013
Borisov, D. I.
2002
The spectrum of a periodic operator with a small localized perturbation. Zbl 1175.34106
Borisov, D. I.; Gadyl’shin, R. R.
2007
Discrete spectrum of the Schrödinger operator perturbed by a narrowly supported potential. Zbl 1178.35144
Bikmetov, A. R.; Borisov, D. I.
2005
On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition. Zbl 1346.35054
Borisov, D. I.; Sharapov, T. F.
2016
Creation of spectral bands for a periodic domain with small windows. Zbl 1342.81143
Borisov, D. I.
2016
Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics. Zbl 1335.35162
Borisov, D. I.
2015
Spectral localization for quantum Hamiltonians with weak random delta interaction. (Localisation spectrale pour des hamiltoniens quantiques, avec une faible interaction aléatoire delta.) Zbl 1401.35218
Borisov, Denis I.; Täufer, Matthias; Veselić, Ivan
2018
Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip. Zbl 1432.35062
Borisov, D. I.
2019
Asymptotic analysis of mean exit time for dynamical systems with a single well potential. Zbl 1441.35020
Borisov, D.; Sultanov, O.
2020
Mathematical and physical meaning of the crossings of energy levels in $$\mathcal {PT}$$-symmetric systems. Zbl 1402.81149
Borisov, Denis I.; Znojil, Miloslav
2016
Estimates of initial scales for layers with small random negative-definite perturbations. Zbl 1440.60058
Borisov, D. I.
2019
Kink scattering from a parity-time-symmetric defect in the $$\phi^4$$ model. Zbl 07246123
Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.; Fatykhov, Minnekhan A.; Javidan, Kurosh
2015
Analytic continuation of resolvents of elliptic operators in a multidimensional cylinder. Zbl 07251966
Borisov, D. I.; Golovina, A. M.; Mukhametrakhimova, A. I.
2020
Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. Zbl 1463.34127
Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna
2019
On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. Zbl 1458.81018
Borisov, D. I.; Golovina, A. M.
2021
Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations. Zbl 1468.35050
Borisov, D. I.; Zezyulin, D. A.; Znojil, M.
2021
On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. Zbl 1458.81018
Borisov, D. I.; Golovina, A. M.
2021
Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations. Zbl 1468.35050
Borisov, D. I.; Zezyulin, D. A.; Znojil, M.
2021
Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. Zbl 1427.81028
Borisov, D. I.; Zezyulin, D. A.
2020
On a model graph with a loop and small edges. Holomorphy property of resolvent. Zbl 1458.34059
Borisov, D. I.; Mukhametrakhimova, A. I.
2020
Asymptotic analysis of mean exit time for dynamical systems with a single well potential. Zbl 1441.35020
Borisov, D.; Sultanov, O.
2020
Analytic continuation of resolvents of elliptic operators in a multidimensional cylinder. Zbl 07251966
Borisov, D. I.; Golovina, A. M.; Mukhametrakhimova, A. I.
2020
Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. Zbl 1426.34039
Borisov, D. I.; Konyrkulzhaeva, M. N.
2019
Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction. Zbl 1430.35169
Borisov, D. I.
2019
Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip. Zbl 1432.35062
Borisov, D. I.
2019
Estimates of initial scales for layers with small random negative-definite perturbations. Zbl 1440.60058
Borisov, D. I.
2019
Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. Zbl 1463.34127
Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna
2019
The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes. Zbl 1403.35023
Borisov, D. I.; Mukhametrakhimova, A. I.
2018
Two patterns of $$\mathcal{PT}$$-symmetry breakdown in a non-numerical six-state simulation. Zbl 1390.81172
Znojil, Miloslav; Borisov, Denis I.
2018
Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip. Zbl 1405.35020
Borisov, D. I.
2018
Expansion of the spectrum in the weak disorder regime for random operators in continuum space. Zbl 1386.35291
Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan
2018
Spectral localization for quantum Hamiltonians with weak random delta interaction. (Localisation spectrale pour des hamiltoniens quantiques, avec une faible interaction aléatoire delta.) Zbl 1401.35218
Borisov, Denis I.; Täufer, Matthias; Veselić, Ivan
2018
Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. Zbl 1381.35027
Borisov, Denis; Tautenhahn, Martin; Veselić, Ivan
2017
On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation. Zbl 1364.35305
Borisov, D. I.; Dmitriev, S. V.
2017
On eigenvalues of a $$\mathcal{PT}$$-symmetric operator in a thin layer. Zbl 1371.35178
Borisov, Denis I.; Znojil, Miloslav
2017
Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. Zbl 1361.35021
Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana
2016
Existence of the stationary solution of a Rayleigh-type equation. Zbl 1408.35118
Borisov, D. I.; Gaydukov, R. K.
2016
Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate. Zbl 1348.82039
Borisov, Denis; Golovina, Anastasia; Veselić, Ivan
2016
Expansion of the almost sure spectrum in the weak disorder regime. Zbl 1331.82026
Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan
2016
On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition. Zbl 1346.35054
Borisov, D. I.; Sharapov, T. F.
2016
Creation of spectral bands for a periodic domain with small windows. Zbl 1342.81143
Borisov, D. I.
2016
Mathematical and physical meaning of the crossings of energy levels in $$\mathcal {PT}$$-symmetric systems. Zbl 1402.81149
Borisov, Denis I.; Znojil, Miloslav
2016
On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows. Zbl 1319.35134
Borisov, D. I.
2015
Multiply degenerate exceptional points and quantum phase transitions. Zbl 1329.81037
Borisov, Denis I.; Ružička, František; Znojil, Miloslav
2015
Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. Zbl 1339.81037
Borisov, D.; Tautenhahn, M.; Veselić, I.
2015
Multiscale unique continuation properties of eigenfunctions. Zbl 1337.35031
Borisov, Denis; Nakić, Ivica; Rose, Christian; Tautenhahn, Martin; Veselić, Ivan
2015
Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics. Zbl 1335.35162
Borisov, D. I.
2015
Kink scattering from a parity-time-symmetric defect in the $$\phi^4$$ model. Zbl 07246123
Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.; Fatykhov, Minnekhan A.; Javidan, Kurosh
2015
Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Zbl 1304.35058
Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana
2014
Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics. Zbl 1282.35033
Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe
2013
Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. Zbl 1269.81050
Borisov, Denis; Pankrashkin, Konstantin
2013
Gap opening and split band edges in waveguides coupled by a periodic system of small windows. Zbl 1288.81046
Borisov, D. I.; Pankrashkin, K. V.
2013
Uniform resolvent convergence for strip with fast oscillating boundary. Zbl 1286.35025
Borisov, Denis; Cardone, Giuseppe; Faella, Luisa; Perugia, Carmen
2013
Low lying eigenvalues of randomly curved quantum waveguides. Zbl 1292.81051
Borisov, Denis; Veselić, Ivan
2013
Tunneling resonances in systems without a classical trapping. Zbl 1280.81035
Borisov, D.; Exner, P.; Golovina, A.
2013
On the extrema of band functions in periodic waveguides. Zbl 1308.34111
Borisov, D. I.; Pankrashkin, K. V.
2013
Asymptotics for the expected lifetime of Brownian motion on thin domains in $$\mathbb R^n$$. Zbl 1296.60220
Borisov, Denis; Freitas, Pedro
2013
On a $$\mathcal{PT}$$-symmetric waveguide with a pair of small holes. Zbl 1321.47166
Borisov, D. I.
2013
On the spectrum of deformations of compact double-sided flat hypersurfaces. Zbl 1282.35261
Borisov, Denis; Freitas, Pedro
2013
The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Zbl 1241.47042
Borisov, Denis; Krejčiřík, David
2012
Planar waveguide with “twisted” boundary conditions: small width. Zbl 1274.81108
Borisov, Denis; Cardone, Giuseppe
2012
Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. Zbl 1290.81038
Borisov, D.; Bunoiu, R.; Cardone, G.
2011
Planar waveguide with ”twisted” boundary conditions: Discrete spectrum. Zbl 1273.81100
Borisov, Denis; Cardone, Giuseppe
2011
On the spectrum of a two-dimensional periodic operator with a small localized perturbation. Zbl 1233.35066
Borisov, D. I.
2011
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods. Zbl 1223.35248
Borisov, Denis; Cardone, Giuseppe
2011
On a waveguide with an infinite number of small windows. (Sur un guide d’onde avec un nombre infini de petites fentes.) Zbl 1211.35098
Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe
2011
Low lying spectrum of weak-disorder quantum waveguides. Zbl 1208.82089
Borisov, Denis; Veselić, Ivan
2011
Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in $$\mathbb R^d$$. Zbl 1180.35397
Borisov, Denis; Freitas, Pedro
2010
On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Zbl 1210.82077
Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe
2010
Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Zbl 1168.35401
Borisov, Denis; Freitas, Pedro
2009
Homogenization of the planar waveguide with frequently alternating boundary conditions. Zbl 1178.81088
Borisov, D.; Cardone, G.
2009
Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Zbl 1181.35151
Borisov, Denis; Freitas, Pedro
2009
Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Zbl 1206.35029
Borisov, D.
2009
$$\mathcal {PT}$$-symmetric waveguides. Zbl 1178.35141
Borisov, Denis; Krejčiřík, David
2008
On the spectrum of a periodic operator with a small localized perturbation. Zbl 1169.34056
Borisov, D. I.; Gadyl&rsquo;shin, R. R.
2008
Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. Zbl 1185.35155
Borisov, Denis
2007
Distant perturbations of the Laplacian in a multi-dimensional space. Zbl 1143.35075
Borisov, Denis I.
2007
The spectrum of two quantum layers coupled by a window. Zbl 1115.81024
Borisov, D.
2007
Some singular perturbations of periodic operators. Zbl 1147.34060
Borisov, D. I.
2007
The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis. Zbl 1137.34039
Borisov, D. I.; Gadyl&rsquo;shin, R. R.
2007
The spectrum of a periodic operator with a small localized perturbation. Zbl 1175.34106
Borisov, D. I.; Gadyl&rsquo;shin, R. R.
2007
Discrete spectrum of an asymmetric pair of waveguides coupled through a window. Zbl 1156.35066
Borisov, D. I.
2006
Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043
Borisov, D.; Exner, P.
2006
The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Zbl 1177.34107
Borisov, D. I.; Gadyl&rsquo;shin, R. R.
2006
On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Zbl 1210.34071
Borisov, D. I.
2006
On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential. Zbl 1134.34337
Borisov, D. I.
2006
Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions. Zbl 1077.81038
Borisov, Denis; Ekholm, Tomas; Kovařík, Hynek
2005
Discrete spectrum of the Schrödinger operator perturbed by a narrowly supported potential. Zbl 1178.35144
Bikmetov, A. R.; Borisov, D. I.
2005
Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008
Borisov, D.; Exner, P.
2004
Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions. Zbl 1108.35032
Borisov, D. I.
2004
On a model boundary value problem for Laplacian with frequently alternating type of boundary condition. Zbl 1137.35308
Borisov, Denis I.
2003
Asymptotics and estimates for the eigenelements of the Laplacian with frequent nonperiod change of boundary conditions. Zbl 1067.35055
Borisov, D. I.
2003
Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094
Borisov, D.; Exner, P.; Gadyl&rsquo;shin, R.
2002
Boundary-value problem in a cylinder with frequently changing type of boundary conditions. Zbl 1045.35047
Borisov, D. I.
2002
On a Laplacian with frequently nonperiodically alternating boundary conditions. Zbl 1197.35027
Borisov, D. I.
2002
On a singularly perturbed boundary value problem for the Laplacian in a cylinder. Zbl 1274.35013
Borisov, D. I.
2002
Bound states in weakly deformed strips and layers. Zbl 1043.35046
Borisov, D.; Exner, P.; Gadyl&rsquo;shin, R.; Krejčiřík, D.
2001
Two-parameter asymptotics in a boundary value problem for the Laplacian. Zbl 1140.35544
Borisov, D. I.
2001
On the spectrum of the Laplacian with frequently alternating boundary conditions. Zbl 0945.35066
Borisov, D. I.; Gadyl&rsquo;shin, R. R.
1999
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### Cited by 214 Authors

 61 Borisov, Denis Ivanovich 32 Nazarov, Sergeĭ Aleksandrovich 18 Cardone, Giuseppe 14 Krejčiřík, David 13 Veselić, Ivan 9 Golovina, Anastasiya Mihajlovna 8 Chechkin, Gregory Aleksandrovich 8 Exner, Pavel 8 Gadyl’shin, Rustem R. 7 Siegl, Petr 6 Freitas, Pedro 6 Weinstein, Michael I. 6 Yang, Chuanfu 5 Bikmetov, Aĭdar Renatovich 5 Khrabustovskyi, Andrii 5 Khusnullin, Il’fat Khamzievich 5 Mukhametrakhimova, A. I. 4 Bunoiu, Renata 4 Drouot, Alexis 4 Konyrkulzhaeva, Maral Nurlanovna 4 Kovařík, Hynek 4 Lotoreichik, Vladimir 4 Najar, Hatem 4 Pankrashkin, Konstantin 4 Pérez-martínez, María-eugenia 4 Taskinen, Jari 4 Täufer, Matthias 4 Tautenhahn, Martin 4 Trynin, Aleksandr Yur’evich 4 Verri, Alessandra A. 3 Beck, Thomas L. 3 Buttazzo, Giuseppe 3 Chechkina, Aleksandra Grigorievna 3 De Maio, Umberto 3 de Oliveira, César R. 3 Durante, Tiziana 3 Fefferman, Charles Louis 3 Gaydukov, R. K. 3 Gómez, Delfina 3 Grushin, V. V. 3 Popov, Igor’ Yur’evich 3 Raymond, Nicolas 3 Royer, Julien 3 Ruotsalainen, Keijo Matti 3 Shaposhnikova, Tatiana A. 3 Siudeja, Bartłomiej Andrzej 3 Znojil, Miloslav 2 Bakharev, Fedor L’vovich 2 Behrndt, Jussi 2 Briani, Luca 2 Briet, Philippe 2 D’Apice, Ciro 2 Duchêne, Vincent 2 Ekholm, Tomas 2 Faella, Luisa 2 Hıra, Fatma 2 Hoecker-Escuti, Francisco 2 Kondej, Sylwia 2 Koroleva, Yu. O. 2 Langer, Matthias 2 Laugesen, Richard Snyder 2 Lee-Thorp, James P. 2 Lu, Jianfeng 2 Marzuola, Jeremy L. 2 Mascarenhas, Maria-Luisa 2 Orive Illera, Rafael 2 Perugia, Carmen 2 Podolskii, Alexander V. 2 Prinari, Francesca 2 Raikov, Georgi D. 2 Rybalko, Yan 2 Senik, Nikita N. 2 Sharapov, Timur Farkhatovich 2 Shepelsky, Dmitry 2 Suslina, Tat’yana Aleksandrovna 2 Uusitalo, Pauliina 2 Vukićević, Iva 2 Wang, Juan 2 Watson, Alexander B. 2 Železný, Jakub 2 Zezyulin, Dmitry A. 2 Zhao, Jie 1 Aiyappan, Srinivasan 1 Akbarfam, Aliasghar Jodayree 1 Akhmetgaliyev, Eldar 1 Alkhutov, Yuriy Alexandrovich 1 Altinisik, Nihat 1 Amirat, Youcef Aït 1 Amore, Paolo 1 Anné, Colette 1 Bao, Gang 1 Barseghyan, Diana 1 Ben Hariz, Samir 1 Blinova, Irina V. 1 Bögli, Sabine 1 Bouchitté, Guy 1 Boyd, John Philip 1 Bruno, Oscar P. 1 Canzani, Yaiza 1 Cassano, Biagio ...and 114 more Authors
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### Cited in 96 Serials

 26 Journal of Mathematical Sciences (New York) 17 Journal of Mathematical Physics 12 Journal of Mathematical Analysis and Applications 11 Journal of Differential Equations 8 St. Petersburg Mathematical Journal 7 Mathematical Notes 7 Journal of Functional Analysis 7 Russian Journal of Mathematical Physics 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Theoretical and Mathematical Physics 6 SIAM Journal on Mathematical Analysis 6 Ufimskiĭ Matematicheskiĭ Zhurnal 5 Journal of Statistical Physics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Annales Henri Poincaré 4 Applicable Analysis 4 Reports on Mathematical Physics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Doklady Mathematics 4 Mathematical Physics, Analysis and Geometry 4 Communications in Contemporary Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Spectral Theory 3 Communications in Mathematical Physics 3 Letters in Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Journal of Computational and Applied Mathematics 3 Transactions of the American Mathematical Society 3 Computational Mathematics and Mathematical Physics 3 Sbornik: Mathematics 3 European Journal of Mechanics. B. Fluids 3 Inverse Problems in Science and Engineering 3 Proceedings of the Steklov Institute of Mathematics 2 International Journal of Theoretical Physics 2 Integral Equations and Operator Theory 2 Mathematika 2 Memoirs of the American Mathematical Society 2 Siberian Mathematical Journal 2 Transactions of the Moscow Mathematical Society 2 Asymptotic Analysis 2 SIAM Journal on Applied Mathematics 2 Calculus of Variations and Partial Differential Equations 2 Journal of Inequalities and Applications 2 Pure and Applied Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Computational Physics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Applied Mathematics and Optimization 1 Journal of the London Mathematical Society. Second Series 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Ricerche di Matematica 1 SIAM Journal on Control and Optimization 1 Studies in Applied Mathematics 1 Zeitschrift für Analysis und ihre Anwendungen 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Journal of Elasticity 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Russian Mathematics 1 Filomat 1 Izvestiya: Mathematics 1 Mathematical Problems in Engineering 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Annals of Mathematics. Second Series 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 The ANZIAM Journal 1 Differential Equations 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Journal of Mathematical Physics, Analysis, Geometry 1 Complex Variables and Elliptic Equations 1 Complex Analysis and Operator Theory 1 Journal of Physics A: Mathematical and Theoretical 1 Networks and Heterogeneous Media 1 Advances in High Energy Physics 1 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 1 Journal of Pseudo-Differential Operators and Applications 1 Eurasian Mathematical Journal 1 Analysis and Mathematical Physics 1 Advances in Nonlinear Analysis 1 Quantum Studies: Mathematics and Foundations 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Cited in 29 Fields

 197 Partial differential equations (35-XX) 88 Quantum theory (81-XX) 70 Operator theory (47-XX) 38 Ordinary differential equations (34-XX) 25 Statistical mechanics, structure of matter (82-XX) 20 Optics, electromagnetic theory (78-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 16 Mechanics of deformable solids (74-XX) 13 Global analysis, analysis on manifolds (58-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Approximations and expansions (41-XX) 6 Probability theory and stochastic processes (60-XX) 6 Numerical analysis (65-XX) 6 Fluid mechanics (76-XX) 3 Combinatorics (05-XX) 3 Differential geometry (53-XX) 2 Algebraic geometry (14-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Relativity and gravitational theory (83-XX) 1 Number theory (11-XX) 1 $$K$$-theory (19-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)