## Katzourakis, Nikolaos I.

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 Author ID: katzourakis.nikolaos-i Published as: Katzourakis, Nikos; Katzourakis, Nikolaos I.; Katzourakis, Nicholas Homepage: http://www.reading.ac.uk/maths-and-stats/about/Staff/n-katzourakis.aspx External Links: MGP · ORCID
 Documents Indexed: 46 Publications since 2011, including 2 Books Reviewing Activity: 13 Reviews Co-Authors: 13 Co-Authors with 18 Joint Publications 192 Co-Co-Authors
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### Co-Authors

 28 single-authored 4 Ayanbayev, Birzhan 4 Pryer, Tristan 3 Abugirda, Hussien 1 Alikakos, Nicholas D. 1 Clark, Ed 1 Croce, Gisella 1 Manfredi, Juan J. 1 Moser, Roger 1 Muha, Boris 1 Parini, Enea 1 Pisante, Giovanni 1 Shaw, Giles 1 Vărvărucă, Eugen
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### Serials

 4 NoDEA. Nonlinear Differential Equations and Applications 3 Calculus of Variations and Partial Differential Equations 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Advances in Nonlinear Analysis 2 Journal of Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the American Mathematical Society 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Communications on Pure and Applied Analysis 2 Advances in Calculus of Variations 1 Archive for Rational Mechanics and Analysis 1 Nonlinearity 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Optimization 1 Le Matematiche 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Numerical Methods for Partial Differential Equations 1 Communications in Partial Differential Equations 1 Glasnik Matematički. Serija III 1 SIAM Journal on Mathematical Analysis 1 Electronic Journal of Differential Equations (EJDE) 1 Discrete and Continuous Dynamical Systems 1 Vietnam Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Hyperbolic Differential Equations 1 S$$\vec{\text{e}}$$MA Journal 1 SpringerBriefs in Mathematics
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### Fields

 40 Partial differential equations (35-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 5 Potential theory (31-XX) 4 Functions of a complex variable (30-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Differential geometry (53-XX) 3 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

40 Publications have been cited 323 times in 74 Documents Cited by Year
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in $$L^\infty$$. Zbl 1326.35006
Katzourakis, Nikos
2015
$$L^{\infty }$$ variational problems for maps and the Aronsson PDE system. Zbl 1248.35074
Katzourakis, Nikolaos I.
2012
Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in $$L^\infty$$. Zbl 1366.35037
Katzourakis, Nikos
2017
Explicit 2D $$\infty$$-harmonic maps whose interfaces have junctions and corners. Zbl 1278.35057
Katzourakis, Nicholas
2013
On the structure of $$\infty$$-harmonic maps. Zbl 1304.49038
Katzourakis, Nikos
2014
$$\infty$$-minimal submanifolds. Zbl 1301.35029
Katzourakis, Nikolaos I.
2014
On the numerical approximation of $$\infty$$-harmonic mappings. Zbl 1371.35068
Katzourakis, Nikos; Pryer, Tristan
2016
Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems. Zbl 1362.35105
Katzourakis, Nikos
2017
Optimal $$\infty$$-quasiconformal immersions. Zbl 1317.30029
Katzourakis, Nikos
2015
Nonuniqueness in vector-valued calculus of variations in $$L^\infty$$ and some linear elliptic systems. Zbl 1316.31017
Katzourakis, Nikos
2015
A characterisation of $$\infty$$-harmonic and $$p$$-harmonic maps via affine variations in $$L^{\infty}$$. Zbl 1357.35088
Katzourakis, Nikos
2017
$$\mathcal{D}$$-solutions to the system of vectorial calculus of variations in $$L^\infty$$ via the singular value problem. Zbl 1386.35081
Pisante, Giovanni; Katzourakis, Nikos; Croce, Gisella
2017
Existence of $$1D$$ vectorial absolute minimisers in $$L^\infty$$ under minimal assumptions. Zbl 1362.35128
Abugirda, Hussien; Katzourakis, Nikos
2017
Heteroclinic travelling waves of gradient diffusion systems. Zbl 1227.35119
Alikakos, Nicholas D.; Katzourakis, Nikolaos I.
2011
Existence, uniqueness and structure of second order absolute minimisers. Zbl 1407.49002
Katzourakis, Nikos; Moser, Roger
2019
The subelliptic $$\infty$$-Laplace system on Carnot-Carathéodory spaces. Zbl 1277.35141
Katzourakis, Nicholas
2013
The eigenvalue problem for the $$\infty$$-Bilaplacian. Zbl 06832644
Katzourakis, Nikos; Parini, Enea
2017
Explicit singular viscosity solutions of the Aronsson equation. Zbl 1230.35037
Katzourakis, Nikolaos I.
2011
Second-order $$L^\infty$$ variational problems and the $$\infty$$-polylaplacian. Zbl 1437.49006
Katzourakis, Nikos; Pryer, Tristan
2020
On the numerical approximation of $$p$$-biharmonic and $$\infty$$-biharmonic functions. Zbl 1419.65113
Katzourakis, Nikos; Pryer, Tristan
2019
An $$L^\infty$$ regularization strategy to the inverse source identification problem for elliptic equations. Zbl 1414.35066
Katzourakis, Nikos
2019
Inverse optical tomography through PDE constrained optimization $$L^\infty$$. Zbl 1430.49037
Katzourakis, Nikos
2019
An illustrative introduction to modern analysis. Zbl 06805410
Katzourakis, Nikos; Vărvărucă, Eugen
2018
Remarks on the maximum principle for the $$\infty$$-Laplacian. Zbl 1375.35155
Katzourakis, Nikos; Manfredi, Juan
2016
Existence and uniqueness of global solutions to fully nonlinear first order elliptic systems. Zbl 1309.35019
Katzourakis, Nikos
2015
Existence and uniqueness of global strong solutions to fully nonlinear second order elliptic systems. Zbl 1358.35031
Katzourakis, Nikos
2016
Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in $$L^{\infty}$$. Zbl 1437.35158
Katzourakis, Nikos
2019
A pointwise characterisation of the PDE system of vectorial calculus of variations in $$L^\infty$$. Zbl 1444.35058
Ayanbayev, Birzhan; Katzourakis, Nikos
2020
Nonsmooth convex functionals and feeble viscosity solutions of singular Euler-Lagrange equations. Zbl 1328.49011
Katzourakis, Nikos
2015
Maximum principles for vectorial approximate minimizers of nonconvex functionals. Zbl 1272.49039
Katzourakis, Nikolaos I.
2013
Counterexamples in calculus of variations in $$L^{\infty}$$ through the vectorial eikonal equation. (Contre-exemples dans le calcul des variations dans $$L^{\infty}$$ par l’équation iconale vectorielle.) Zbl 1390.49014
Katzourakis, Nikos; Shaw, Giles
2018
On the Dirichlet problem for fully nonlinear elliptic Hessian systems. Zbl 1358.35026
Katzourakis, Nikos
2016
A minimisation problem in $$L^\infty$$ with PDE and unilateral constraints. Zbl 1451.35240
Katzourakis, Nikos
2020
A Hölder continuous nowhere improvable function with derivative singular distribution. Zbl 1260.35051
Katzourakis, Nikolaos I.
2012
Weak vs. $$\mathcal{D}$$-solutions to linear hyperbolic first-order systems with constant coefficients. Zbl 1406.35171
Katzourakis, Nikos
2018
Vectorial variational principles in $$L^\infty$$ and their characterisation through PDE systems. Zbl 1465.35174
Ayanbayev, Birzhan; Katzourakis, Nikos
2021
On the loss of compactness in the vectorial heteroclinic connection problem. Zbl 1354.34078
Katzourakis, Nikos
2016
On linear degenerate elliptic PDE systems with constant coefficients. Zbl 1343.35117
Katzourakis, Nikos
2016
On the well-posedness of global fully nonlinear first order elliptic systems. Zbl 1392.35120
Abugirda, Hussien; Katzourakis, Nikos
2018
Vectorial variational problems in $$L^\infty$$ constrained by the Navier-Stokes equations. Zbl 1481.35307
Clark, Ed; Katzourakis, Nikos; Muha, Boris
2022
Vectorial variational problems in $$L^\infty$$ constrained by the Navier-Stokes equations. Zbl 1481.35307
Clark, Ed; Katzourakis, Nikos; Muha, Boris
2022
Vectorial variational principles in $$L^\infty$$ and their characterisation through PDE systems. Zbl 1465.35174
Ayanbayev, Birzhan; Katzourakis, Nikos
2021
Second-order $$L^\infty$$ variational problems and the $$\infty$$-polylaplacian. Zbl 1437.49006
Katzourakis, Nikos; Pryer, Tristan
2020
A pointwise characterisation of the PDE system of vectorial calculus of variations in $$L^\infty$$. Zbl 1444.35058
Ayanbayev, Birzhan; Katzourakis, Nikos
2020
A minimisation problem in $$L^\infty$$ with PDE and unilateral constraints. Zbl 1451.35240
Katzourakis, Nikos
2020
Existence, uniqueness and structure of second order absolute minimisers. Zbl 1407.49002
Katzourakis, Nikos; Moser, Roger
2019
On the numerical approximation of $$p$$-biharmonic and $$\infty$$-biharmonic functions. Zbl 1419.65113
Katzourakis, Nikos; Pryer, Tristan
2019
An $$L^\infty$$ regularization strategy to the inverse source identification problem for elliptic equations. Zbl 1414.35066
Katzourakis, Nikos
2019
Inverse optical tomography through PDE constrained optimization $$L^\infty$$. Zbl 1430.49037
Katzourakis, Nikos
2019
Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in $$L^{\infty}$$. Zbl 1437.35158
Katzourakis, Nikos
2019
An illustrative introduction to modern analysis. Zbl 06805410
Katzourakis, Nikos; Vărvărucă, Eugen
2018
Counterexamples in calculus of variations in $$L^{\infty}$$ through the vectorial eikonal equation. (Contre-exemples dans le calcul des variations dans $$L^{\infty}$$ par l’équation iconale vectorielle.) Zbl 1390.49014
Katzourakis, Nikos; Shaw, Giles
2018
Weak vs. $$\mathcal{D}$$-solutions to linear hyperbolic first-order systems with constant coefficients. Zbl 1406.35171
Katzourakis, Nikos
2018
On the well-posedness of global fully nonlinear first order elliptic systems. Zbl 1392.35120
Abugirda, Hussien; Katzourakis, Nikos
2018
Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in $$L^\infty$$. Zbl 1366.35037
Katzourakis, Nikos
2017
Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems. Zbl 1362.35105
Katzourakis, Nikos
2017
A characterisation of $$\infty$$-harmonic and $$p$$-harmonic maps via affine variations in $$L^{\infty}$$. Zbl 1357.35088
Katzourakis, Nikos
2017
$$\mathcal{D}$$-solutions to the system of vectorial calculus of variations in $$L^\infty$$ via the singular value problem. Zbl 1386.35081
Pisante, Giovanni; Katzourakis, Nikos; Croce, Gisella
2017
Existence of $$1D$$ vectorial absolute minimisers in $$L^\infty$$ under minimal assumptions. Zbl 1362.35128
Abugirda, Hussien; Katzourakis, Nikos
2017
The eigenvalue problem for the $$\infty$$-Bilaplacian. Zbl 06832644
Katzourakis, Nikos; Parini, Enea
2017
On the numerical approximation of $$\infty$$-harmonic mappings. Zbl 1371.35068
Katzourakis, Nikos; Pryer, Tristan
2016
Remarks on the maximum principle for the $$\infty$$-Laplacian. Zbl 1375.35155
Katzourakis, Nikos; Manfredi, Juan
2016
Existence and uniqueness of global strong solutions to fully nonlinear second order elliptic systems. Zbl 1358.35031
Katzourakis, Nikos
2016
On the Dirichlet problem for fully nonlinear elliptic Hessian systems. Zbl 1358.35026
Katzourakis, Nikos
2016
On the loss of compactness in the vectorial heteroclinic connection problem. Zbl 1354.34078
Katzourakis, Nikos
2016
On linear degenerate elliptic PDE systems with constant coefficients. Zbl 1343.35117
Katzourakis, Nikos
2016
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in $$L^\infty$$. Zbl 1326.35006
Katzourakis, Nikos
2015
Optimal $$\infty$$-quasiconformal immersions. Zbl 1317.30029
Katzourakis, Nikos
2015
Nonuniqueness in vector-valued calculus of variations in $$L^\infty$$ and some linear elliptic systems. Zbl 1316.31017
Katzourakis, Nikos
2015
Existence and uniqueness of global solutions to fully nonlinear first order elliptic systems. Zbl 1309.35019
Katzourakis, Nikos
2015
Nonsmooth convex functionals and feeble viscosity solutions of singular Euler-Lagrange equations. Zbl 1328.49011
Katzourakis, Nikos
2015
On the structure of $$\infty$$-harmonic maps. Zbl 1304.49038
Katzourakis, Nikos
2014
$$\infty$$-minimal submanifolds. Zbl 1301.35029
Katzourakis, Nikolaos I.
2014
Explicit 2D $$\infty$$-harmonic maps whose interfaces have junctions and corners. Zbl 1278.35057
Katzourakis, Nicholas
2013
The subelliptic $$\infty$$-Laplace system on Carnot-Carathéodory spaces. Zbl 1277.35141
Katzourakis, Nicholas
2013
Maximum principles for vectorial approximate minimizers of nonconvex functionals. Zbl 1272.49039
Katzourakis, Nikolaos I.
2013
$$L^{\infty }$$ variational problems for maps and the Aronsson PDE system. Zbl 1248.35074
Katzourakis, Nikolaos I.
2012
A Hölder continuous nowhere improvable function with derivative singular distribution. Zbl 1260.35051
Katzourakis, Nikolaos I.
2012
Heteroclinic travelling waves of gradient diffusion systems. Zbl 1227.35119
Alikakos, Nicholas D.; Katzourakis, Nikolaos I.
2011
Explicit singular viscosity solutions of the Aronsson equation. Zbl 1230.35037
Katzourakis, Nikolaos I.
2011
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### Cited by 87 Authors

 37 Katzourakis, Nikolaos I. 6 Pryer, Tristan 5 Ayanbayev, Birzhan 3 Abugirda, Hussien 2 Prinari, Francesca 2 Siltakoski, Jarkko 1 Alama, Stan 1 Belak, Christoph 1 Bidaut-Veron, Marie-Françoise 1 Bronsard, Lia 1 Brustad, Karl K. 1 Calder, Jeff 1 Cantin, Guillaume 1 Chaudhary, Sudhakar 1 Chen, Chiun-Chuan 1 Chien, Hung-Yu 1 Christensen, Soren 1 Clark, Ed 1 Contreras, Andres A. 1 Cook, Brendan 1 Cotter, Colin John 1 Courte, Luca 1 Croce, Gisella 1 Dadok, Jiri 1 Deasy, Jacob 1 Dondl, Patrick Werner 1 Drivaliaris, Dimosthenis 1 Dumitrescu, Roxana 1 Einkemmer, Lukas 1 Eleuteri, Michela 1 Esteve, Carlos 1 García-Huidobro, Marta 1 Gui, Changfeng 1 Hayrapetyan, Gurgen 1 Heino, Joonas 1 Huang, Chih-Chiang 1 Janeček, Karel 1 Karagiorgos, Yiannis 1 Li, Zheng 1 Liao, Dongni 1 Manfredi, Juan J. 1 Medina, Maria 1 Miller, Christopher W. 1 Molina-Fructuoso, Martin 1 Morrison, George 1 Moser, Roger 1 Muha, Boris 1 Murray, Ryan W. 1 Neilan, Michael 1 Ochoa, Pablo D. 1 Ostermann, Alexander 1 Papamikos, Georgios A. 1 Parini, Enea 1 Parviainen, Mikko 1 Pawlaschyk, Thomas Patrick 1 Peng, Fa 1 Pisante, Giovanni 1 Promislow, Keith Steven 1 Puglisi, Daniele 1 Rajashekar, Naraveni 1 Reisinger, Christoph 1 Salgado, Abner J. 1 Seifried, Frank Thomas 1 Shaw, Giles 1 Sîrbu, Mihai 1 Sourdis, Christos 1 Srinivas Kumar, V. V. K. 1 Stefanelli, Ulisse 1 Sternberg, Peter J. 1 Taheri, Ali 1 Thorel, Alexandre 1 Tkachev, Vladimir G. 1 Vazquez, Juan Luis 1 Véron, Laurent 1 Wang, Changyou 1 Wang, Jialin 1 Wu, Shimin 1 Yang, Insoon 1 Yang, Qiang 1 Yannakakis, Nikolaos 1 Zappale, Elvira 1 Zeron, Eduardo Santillan 1 Zhang, Wujun 1 Zhang, Yufei 1 Zhao, Mingfeng 1 Zhou, Yuan 1 Zuazua, Enrique
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### Cited in 46 Serials

 4 Journal of Differential Equations 4 Calculus of Variations and Partial Differential Equations 4 NoDEA. Nonlinear Differential Equations and Applications 3 Nonlinearity 3 Proceedings of the American Mathematical Society 3 SIAM Journal on Control and Optimization 3 SIAM Journal on Mathematical Analysis 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Advances in Calculus of Variations 3 Advances in Nonlinear Analysis 2 Applied Mathematics and Optimization 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Discrete and Continuous Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Boundary Value Problems 1 Archive for Rational Mechanics and Analysis 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of Optimization Theory and Applications 1 Le Matematiche 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Studies in Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Numerical Methods for Partial Differential Equations 1 Communications in Partial Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 Vietnam Journal of Mathematics 1 Communications in Contemporary Mathematics 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Nonlinear Analysis. Real World Applications 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Hyperbolic Differential Equations 1 Mediterranean Journal of Mathematics 1 Acta Numerica 1 SIAM Journal on Financial Mathematics 1 S$$\vec{\text{e}}$$MA Journal 1 Journal of Elliptic and Parabolic Equations 1 SIAM Journal on Mathematics of Data Science
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### Cited in 26 Fields

 62 Partial differential equations (35-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 7 Numerical analysis (65-XX) 6 Operator theory (47-XX) 5 Potential theory (31-XX) 5 Probability theory and stochastic processes (60-XX) 5 Systems theory; control (93-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Functions of a complex variable (30-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Nonassociative rings and algebras (17-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX)