Nikos Katzourakis
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+44 (0) 118 378 7463
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Associate Professor
Departmental Director of Postgraduate Studies
Office
Room 107Building location
MathematicsAreas of interest
- Analysis of Nonlinear PDE, in particular Fully Nonlinear systems, (Quasi)linear Non-divergence form systems and Differential Inclusions
- Calculus of Variations, in particular Vector-valued Calculus of Variations in the space L-Infinity and Nonconvex Variational Integrals
- Applications of the above to Geometric Analysis, Data Assimilation, Automotive Engineering, Electromobility, Biomedical Imaging and the Earth Sciences
Teaching
Current teaching (2021/22):
Research centres and groups
Professional bodies/affiliations
LMS-CMI Research School
- Modern Topics in Nonlinear PDE and Geometric Analysis
EPSRC Network
Websites/blogs
Selected publications
- Textbook in Analysis (CRC Press, Taylor & Francis Group, with E. Varvaruca, 2018)
An Illustrative Introduction to Modern Analysis - Springer Monograph (Brief 2015)
An Introduction to Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
Publications
- 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
- 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://dx.doi.org/10.4171/ZAA/1699
- Katzourakis, N. (2022) Generalised vectorial ∞-eigenvalue non linear problems for L∞ functionals. Nonlinear Analysis: Theory, Methods & Applications , 219 ISSN: 0362-546X | doi: https://dx.doi.org/10.1016/j.na.2022.112806
- Clark, E. , Katzourakis, N. , 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://dx.doi.org/10.1088/1361-6544/ac372a
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Ayanbayev, B.
and
Katzourakis, N.
ORCID: 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://dx.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://dx.doi.org/10.1007/s00245-019-09569-y
- Abugirda, H. , Ayanbayev, B. , 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://dx.doi.org/10.1216/rmj.2020.50.383
- Katzourakis, N. (2020) A minimisation problem in L∞ with PDE and unilateral constraints. ESAIM Control Optimization & Calculus of Variations , 26 ISSN: 1262-3377 | doi: https://dx.doi.org/10.1051/cocv/2019034
- 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://dx.doi.org/10.1515/acv-2016-0052
- 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://dx.doi.org/10.1017/prm.2018.89
- 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://dx.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://dx.doi.org/10.1137/18M1226373
- 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://dx.doi.org/10.1007/s00205-018-1305-6
- 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://dx.doi.org/10.1002/num.22295
- 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://dx.doi.org/10.1515/anona-2016-0164
- 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://dx.doi.org/10.1016/j.crma.2018.04.010
- 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://dx.doi.org/10.1142/S0219891618500121
- 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 ISSN: 2052-532X | doi: https://dx.doi.org/10.23952/jnfa.2018.6
- 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://dx.doi.org/10.1515/anona-2016-0049
- Katzourakis, N. and Parini, E. (2017) The eigenvalue problem for the ∞-Bilaplacian. Nonlinear differential equations and applications , 24 (6). ISSN: 1420-9004 | doi: https://dx.doi.org/10.1007/s00030-017-0492-4
- Katzourakis, N. and Varvaruca, E. (2017) An illustrative introduction to modern analysis. Taylor and Francis - CRC Press pp 558. ISBN: 9781138718272
- Croce, G. , Katzourakis, N. , 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://dx.doi.org/10.3934/dcds.2017266
- 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://dx.doi.org/10.1016/j.jde.2017.02.048
- 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. (2017) Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in L∞. Calculus of Variations and Partial Differential Equations , 56 ISSN: 1432-0835 | doi: https://dx.doi.org/10.1007/s00526-016-1099-z
- 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://dx.doi.org/10.3336/gm.52.1.08
- 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://dx.doi.org/10.1090/proc/13421
- Katzourakis, N. and Pryer, T. (2016) On the numerical approximation of ∞-harmonic mappings. Nonlinear differential equations and applications , 23 (6). ISSN: 1420-9004 | doi: https://dx.doi.org/10.1007/s00030-016-0415-9
- Katzourakis, N. (2016) Existence and uniqueness of global solutions to fully nonlinear second order elliptic systems. Nonlinear differential equations and applications , 23 (3). ISSN: 1420-9004 | doi: https://dx.doi.org/10.1007/s00030-016-0381-2
- 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://dx.doi.org/10.1515/acv-2015-0004
- 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://dx.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://dx.doi.org/10.2422/2036-2145.201411_003
- 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://dx.doi.org/10.1017/S0308210515000700
- 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://dx.doi.org/10.1016/j.na.2014.12.002
- 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://dx.doi.org/10.1007/s00526-014-0786-x
- 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://dx.doi.org/10.3934/cpaa.2015.14.313
- Katzourakis, N. (2015) Optimal infinity-quasiconformal immersions. ESAIM Control Optimization & Calculus of Variations , 21 (2). pp. 561-582. ISSN: 1262-3377 | doi: https://dx.doi.org/10.1051/cocv/2014038
- 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
- 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://dx.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. (2013) The subelliptic Infinity-Laplace system on Carnot-Caratheodory Spaces. Advances in Nonlinear Analysis , 2 (2). pp. 213-233. ISSN: 2191-950x | doi: https://dx.doi.org/10.1515/anona-2013-0004
- Katzourakis, N. (2013) Infinity-minimal submanifolds. Proceedings of the American Mathematical Society , 142 (8). pp. 2797-2811. ISSN: 0002-9939
- Katzourakis, N. (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://dx.doi.org/10.1007/s00526-012-0491-6
- Katzourakis, N. (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://dx.doi.org/10.1007/BF03322609
- Katzourakis, N. (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://dx.doi.org/10.1016/j.jde.2012.05.012
- Katzourakis, N. (2011) Explicit singular viscosity solutions of the Aronsson equation. Comptes Rendus Mathematique , 349 (21-22). pp. 1173-1176. ISSN: 1631-073X | doi: https://dx.doi.org/10.1016/j.crma.2011.10.010
- Katzourakis, N. (2011) Heteroclinic travelling waves of gradient diffusion systems. Transactions of the American Mathematical Society , 363 (3). pp. 1365-1397. ISSN: 1088-6850