Article

Clark, E. and Katzourakis, N. (2024) Generalized second order vectorial ∞-eigenvalue problems. Proceedings of the Royal Society of Edinburgh A: Mathematics. ISSN 1473-7124 doi: https://doi.org/10.1017/prm.2024.27

Clark, E. and Katzourakis, N. (2023) On isosupremic vectorial minimisation problems in l∞ with general nonlinear constraints. Advances in Calculus of Variations. ISSN 1864-8266 doi: https://doi.org/10.1515/acv-2022-0068

Katzourakis, N. and Moser, R. (2023) Variational problems in L∞ involving semilinear second order differential operators. ESAIM Control Optimization & Calculus of Variations, 29. 76. ISSN 1262-3377 doi: https://doi.org/10.1051/cocv/2023066

Katzourakis, N. (2022) Generalised vectorial ∞-eigenvalue non linear problems for L∞ functionals. Nonlinear Analysis: Theory, Methods & Applications, 219. 112806. ISSN 0362-546X doi: https://doi.org/10.1016/j.na.2022.112806

Katzourakis, N. (2022) On a vector-valued generalisation of viscosity solutions for general PDE systems. Zeitschrift für Analysis und ihre Anwendungen, 41 (1/2). pp. 93-132. ISSN 1661-4534 doi: https://doi.org/10.4171/ZAA/1699

Clark, E., Katzourakis, N. and Muha, B. (2021) Vectorial variational problems in L ∞ constrained by the Navier–Stokes equations. Nonlinearity, 35 (1). pp. 470-491. ISSN 1361-6544 doi: https://doi.org/10.1088/1361-6544/ac372a

Ayanbayev, B. and Katzourakis, N. ORCID: https://orcid.org/0000-0001-5292-270X (2021) On the inverse source identification problem in L ∞ for fully nonlinear elliptic PDE. Vietnam Journal of Mathematics, 49 (3). pp. 815-829. ISSN 2305-2228 doi: https://doi.org/10.1007/s10013-021-00515-6

Ayanbayev, B. and Katzourakis, N. (2021) Vectorial variational principles in L∞ and their characterisation through PDE systems. Applied Mathematics & Optimization, 83 (2). pp. 833-848. ISSN 1432-0606 doi: https://doi.org/10.1007/s00245-019-09569-y

Katzourakis, N. and Ayanbayev, B. (2020) A pointwise characterisation of the PDE system of vectorial calculus of variations in L∞. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 150 (4). pp. 1653-1669. ISSN 1364-5021 doi: https://doi.org/10.1017/prm.2018.89

Abugirda, H., Ayanbayev, B. and Katzourakis, N. (2020) Rigidity and flatness of the image of certain classes of mappings having tangential laplacian. Rocky Mountain Journal of Mathematics, 50 (2). pp. 383-396. ISSN 0035-7596 doi: https://doi.org/10.1216/rmj.2020.50.383

Katzourakis, N. and Pryer, T. (2020) Second order L∞ variational problems and the ∞-polylapacian. Advances in Calculus of Variations, 13 (2). pp. 115-140. ISSN 1864-8266 doi: https://doi.org/10.1515/acv-2016-0052

Katzourakis, N. (2020) A minimisation problem in L∞ with PDE and unilateral constraints. ESAIM Control Optimization & Calculus of Variations, 26. 60. ISSN 1262-3377 doi: https://doi.org/10.1051/cocv/2019034

Pryer, T. and Katzourakis, N. (2019) On the numerical approximation of p-biharmonic and ∞-biharmonic functions. Numerical Methods for Partial Differential Equations, 35 (1). pp. 155-180. ISSN 1098-2426 doi: https://doi.org/10.1002/num.22295

Katzourakis, N. and Moser, R. (2019) Existence, uniqueness and structure of second order absolute minimisers. Archive for Rational Mechanics and Analysis, 231 (3). pp. 1615-1634. ISSN 0003-9527 doi: https://doi.org/10.1007/s00205-018-1305-6

Katzourakis, N. (2019) Inverse optical tomography through PDE constrained optimisation in L∞. SIAM Journal on Control and Optimization, 57 (6). pp. 4205-4233. ISSN 1095-7138 doi: https://doi.org/10.1137/19M1239908

Katzourakis, N. (2019) An L∞ regularisation strategy to the inverse source identification problem for elliptic equations. SIAM Journal on Mathematical Analysis (SIMA), 51 (2). pp. 1349-1370. ISSN 0036-1410 doi: https://doi.org/10.1137/18M1226373

Katzourakis, N. (2019) Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in L∞. Advances in Nonlinear Analysis, 8 (1). pp. 508-516. ISSN 2191-950X doi: https://doi.org/10.1515/anona-2016-0164

Katzourakis, N. (2018) Weak versus D-solutions to linear hyperbolic first order systems with constant coefficients. Journal of Hyperbolic Differential Equations, 15 (2). pp. 329-347. ISSN 1793-6993 doi: https://doi.org/10.1142/S0219891618500121

Katzourakis, N. and Hussien, A. (2018) On the well-posedness of global fully nonlinear first order elliptic systems. Advances in Nonlinear Analysis, 7 (2). pp. 139-148. ISSN 2191-950X doi: https://doi.org/10.1515/anona-2016-0049

Katzourakis, N. and Shaw, G. (2018) Counterexamples in calculus of variations in L∞ through the vectorial Eikonal equation. Comptes Rendus Mathematique, 356 (5). pp. 498-502. ISSN 1631-073X doi: https://doi.org/10.1016/j.crma.2018.04.010

Katzourakis, N. and Pryer, T. (2018) A review from the PDE viewpoint of Hamilton-Jacobi-Bellman equations arising in optimal control with vectorial cost. Journal of Nonlinear Functional Analysis, 2018. 6. ISSN 2052-532X doi: https://doi.org/10.23952/jnfa.2018.6

Croce, G., Katzourakis, N. and Pisante, G. (2017) D-solutions to the system of vectorial calculus of variations in l∞ via the singular value problem. Discrete and Continuous Dynamical Systems: Series B, 37 (12). pp. 6165-6181. ISSN 1531-3492 doi: https://doi.org/10.3934/dcds.2017266

Katzourakis, N. and Parini, E. (2017) The eigenvalue problem for the ∞-Bilaplacian. Nonlinear differential equations and applications, 24 (6). 68. ISSN 1420-9004 doi: https://doi.org/10.1007/s00030-017-0492-4

Katzourakis, N. (2017) Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems. Journal of Differential Equations, 263 (1). pp. 641-686. ISSN 0022-0396 doi: https://doi.org/10.1016/j.jde.2017.02.048

Abugirda, H. and Katzourakis, N. (2017) Existence of 1D vectorial absolute minimisers in L infinity under minimal assumptions. Proceedings of the American Mathematical Society, 145 (6). pp. 2567-2575. ISSN 0002-9939 doi: https://doi.org/10.1090/proc/13421

Katzourakis, N. (2017) A remark on global W1,p bounds of harmonic functions with Lipschitz boundary values. Glasnik Matematicki, 52 (1). pp. 107-113. ISSN 1846-7989 doi: https://doi.org/10.3336/gm.52.1.08

Katzourakis, N. (2017) Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in L∞. Calculus of Variations and Partial Differential Equations, 56. 15. ISSN 1432-0835 doi: https://doi.org/10.1007/s00526-016-1099-z

Katzourakis, N. (2017) A new characterisation ∞-harmonic AND p-harmonic map↲ s via affine variations in L∞. Electronic Journal of Differential Equations, 2017. pp. 1-19. ISSN 1072-6691

Katzourakis, N. and Pryer, T. (2016) On the numerical approximation of ∞-harmonic mappings. Nonlinear differential equations and applications, 23 (6). 61. ISSN 1420-9004 doi: https://doi.org/10.1007/s00030-016-0415-9

Katzourakis, N. (2016) On linear degenerate elliptic PDE systems with constant coefficients. Advances in Calculus of Variations, 9 (3). pp. 283-291. ISSN 1864-8266 doi: https://doi.org/10.1515/acv-2015-0004

Katzourakis, N. (2016) Existence and uniqueness of global solutions to fully nonlinear second order elliptic systems. Nonlinear differential equations and applications, 23 (3). 33. ISSN 1420-9004 doi: https://doi.org/10.1007/s00030-016-0381-2

Katzourakis, N. (2016) On the loss of compactness in the vectorial heteroclinic connection problem. Proceedings of the Royal Society of Edinburgh A, 146 (3). pp. 595-608. ISSN 1473-7124 doi: https://doi.org/10.1017/S0308210515000700

Katzourakis, N. and Manfredi, J. (2016) Remarks on the validity on the maximum principle for the ∞-Laplacian. Le Matematiche, 71. pp. 63-74. ISSN 2037-5298 doi: https://doi.org/10.4418/2016.71.1.5

Katzourakis, N. (2016) On the Dirichlet problem for fully nonlinear elliptic hessian systems. Annali della Scuola Normale Superiore di Pisa, 16 (3). pp. 707-727. ISSN 2036-2145 doi: https://doi.org/10.2422/2036-2145.201411_003

Katzourakis, N. (2015) Nonsmooth convex functionals and feeble viscosity solutions of singular Euler-Lagrange equations. Calculus of Variations and Partial Differential Equations, 54 (1). pp. 275-298. ISSN 1432-0835 doi: https://doi.org/10.1007/s00526-014-0786-x

Katzourakis, N. (2015) Optimal infinity-quasiconformal immersions. ESAIM Control Optimization & Calculus of Variations, 21 (2). pp. 561-582. ISSN 1262-3377 doi: https://doi.org/10.1051/cocv/2014038

Katzourakis, N. (2015) Existence and uniqueness of global solutions to fully nonlinear first order elliptic systems. Nonlinear Analysis: Theory Methods & Applications, 115. pp. 50-61. ISSN 0362-546X doi: https://doi.org/10.1016/j.na.2014.12.002

Katzourakis, N. (2015) Nonuniqueness in vector-valued calculus of variations in l-infinity and some linear elliptic systems. Communications on Pure and Applied Analysis, 14 (1). pp. 313-327. ISSN 1553-5258 doi: https://doi.org/10.3934/cpaa.2015.14.313

Katzourakis, N. (2014) On the structure of infinity-harmonic maps. Communications in Partial Differential Equations, 39 (11). pp. 2091-2124. ISSN 0360-5302 doi: https://doi.org/10.1080/03605302.2014.920351

Katzourakis, N. (2013) Explicit 2D Infinity-Harmonic maps whose interfaces have junctions and corners. Comptes Rendus Mathematique, 351 (17-18). pp. 677-680. ISSN 1631-073X

Katzourakis, N. I. (2013) Maximum principles for vectorial approximate minimisers on non-convex functionals. Calculus of Variations and Partial Differential Equations, 46 (3-4). pp. 505-522. ISSN 1432-0835 doi: https://doi.org/10.1007/s00526-012-0491-6

Katzourakis, N. I. (2013) Infinity-minimal submanifolds. Proceedings of the American Mathematical Society, 142 (8). pp. 2797-2811. ISSN 0002-9939

Katzourakis, N. I. (2013) The subelliptic Infinity-Laplace system on Carnot-Caratheodory Spaces. Advances in Nonlinear Analysis, 2 (2). pp. 213-233. ISSN 2191-950x doi: https://doi.org/10.1515/anona-2013-0004

Katzourakis, N. I. (2012) L-Infinity variational problems of maps and the Aronsson PDE system. Journal of Differential Equations, 253 (7). pp. 2123-2139. ISSN 0022-0396 doi: https://doi.org/10.1016/j.jde.2012.05.012

Katzourakis, N. I. (2012) A Holder continuous nowhere improvable function with derivative singular distribution. SeMA Journal (Sociecad Espaniola de Matematica Applicada), 59 (1). pp. 37-51. ISSN 2254-3902 doi: https://doi.org/10.1007/BF03322609

Katzourakis, N. I. (2011) Explicit singular viscosity solutions of the Aronsson equation. Comptes Rendus Mathematique, 349 (21-22). pp. 1173-1176. ISSN 1631-073X doi: https://doi.org/10.1016/j.crma.2011.10.010

Katzourakis, N. I. (2011) Heteroclinic travelling waves of gradient diffusion systems. Transactions of the American Mathematical Society, 363 (3). pp. 1365-1397. ISSN 1088-6850

Book

Katzourakis, N. and Varvaruca, E. (2017) An illustrative introduction to modern analysis. Taylor and Francis - CRC Press, pp558. ISBN 9781138718272

Katzourakis, N. (2015) An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l-infinity. SpringerBriefs in Mathematics. Springer, Heidelberg. ISBN 9783319128283