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## Urbas, John Ivan Eugene

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 Author ID: urbas.john-i-e Published as: Urbas, J. I. E.; Urbas, John; Urbas, John I. E. Homepage: https://maths.anu.edu.au/people/academics/john-urbas External Links: MGP · dblp
 Documents Indexed: 42 Publications since 1983 Reviewing Activity: 212 Reviews

#### Co-Authors

 37 single-authored 4 Trudinger, Neil Sidney 2 Lions, Pierre-Louis 1 Sheng, Weimin 1 Wang, Xu-Jia
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#### Serials

 5 Calculus of Variations and Partial Differential Equations 4 Mathematische Zeitschrift 3 Bulletin of the Australian Mathematical Society 3 Journal of Differential Geometry 3 Journal für die Reine und Angewandte Mathematik 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Advances in Differential Equations 1 Communications on Pure and Applied Mathematics 1 Duke Mathematical Journal 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Proceedings of the American Mathematical Society 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Communications in Analysis and Geometry 1 The Asian Journal of Mathematics

#### Fields

 40 Partial differential equations (35-XX) 21 Differential geometry (53-XX) 4 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

36 Publications have been cited 572 times in 379 Documents Cited by Year
On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures. Zbl 0691.35048
Urbas, John I. E.
1990
An expansion of convex hypersurfaces. Zbl 0746.53006
Urbas, John I. E.
1991
On the existence of nonclassical solutions for two classes of fully nonlinear elliptic equations. Zbl 0724.35028
Urbas, John I. E.
1990
On the second boundary value problem for equations of Monge-Ampère type. Zbl 0880.35031
Urbas, John
1997
The Neumann problem for equations of Monge-Ampère type. Zbl 0604.35027
Lions, P.-L.; Trudinger, N. S.; Urbas, J. I. E.
1986
The Dirichlet problem for the equation of prescribed Gauss curvature. Zbl 0524.35047
Trudinger, Neil S.; Urbas, John I. E.
1983
Regularity of generalized solutions of Monge-Ampère equations. Zbl 0617.35017
Urbas, John I. E.
1988
Oblique boundary value problems for equations of Monge-Ampère type. Zbl 0912.35068
Urbas, John
1998
On second derivative estimates for equations of Monge-Ampère type. Zbl 0557.35054
Trudinger, Neil S.; Urbas, John I. E.
1984
Nonlinear oblique boundary value problems for Hessian equations in two dimensions. Zbl 0841.35042
Urbas, John
1995
Interior curvature bounds for a class of curvature equations. Zbl 1174.35378
Sheng, Weimin; Urbas, John; Wang, Xu-Jia
2004
Complete noncompact self-similar solutions of Gauss curvature flows. I: Positive powers. Zbl 0910.53043
Urbas, John
1998
The equation of prescribed Gauss curvature without boundary conditions. Zbl 0566.53013
Urbas, John I. E.
1984
Hessian equations on compact Riemannian manifolds. Zbl 1052.58025
Urbas, John
2002
Convex curves moving homothetically by negative powers of their curvature. Zbl 0970.53039
Urbas, John
1999
Boundary regularity for solutions of the equation of prescribed Gauss curvature. Zbl 0757.35024
Urbas, J. I. E.
1991
Global Hölder estimates for equations of Monge-Ampère type. Zbl 0674.35026
Urbas, John I. E.
1988
An interior second derivative bound for solutions of Hessian equations. Zbl 0986.35035
Urbas, John
2001
The generalized Dirichlet problem for equations of Monge-Ampère type. Zbl 0602.35038
Urbas, John I. E.
1986
The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. Zbl 1080.53062
Urbas, John
2003
The second boundary value problem for a class of Hessian equations. Zbl 1194.35158
Urbas, John
2001
Some interior regularity results for solutions of Hessian equations. Zbl 0965.35056
Urbas, John
2000
Complete noncompact self-similar solutions of Gauss curvature flows. II. Negative powers. Zbl 0957.53033
Urbas, John
1999
Nonlinear oblique boundary value problems for two-dimensional curvature equations. Zbl 0853.35046
Urbas, John
1996
Weingarten hypersurfaces with prescribed gradient image. Zbl 1130.35341
Urbas, John
2002
Correction to: “An expansion of convex hypersurfaces”. Zbl 0777.53011
Urbas, John I. E.
1992
The oblique derivative problem for equations of Monge-Ampere type in two dimensions. Zbl 0649.35038
Urbas, John I. E.
1987
The Neumann problem for equations of Monge-Ampère type. Zbl 0617.35050
Lions, P.-L.; Trudinger, N. S.; Urbas, J. I. E.
1986
Interior curvature bounds for spacelike hypersurfaces of prescribed $$k$$-th mean curvature. Zbl 1079.53094
Urbas, John
2003
An interior curvature bound for hypersurfaces of prescribed $$k$$-th mean curvature. Zbl 0959.53031
Urbas, John
2000
A note on the contact angle boundary condition for Monge-Ampère equations. Zbl 0941.35033
Urbas, John
2000
Regularity of almost extremal solutions of Monge-Ampère equations. Zbl 0735.35036
Urbas, John I. E.
1991
A remark on minimal Lagrangian diffeomorphisms and the Monge-Ampère equation. Zbl 1158.53061
Urbas, John
2007
Monotonicity formulae and curvature equations. Zbl 1075.53034
Urbas, John
2003
Some new estimates for solutions of degenerate two dimensional Monge-Ampère equations. Zbl 1158.35367
Urbas, John
2001
Self-similar solutions of Gauss curvature flows. Zbl 0919.35043
Urbas, John
1999
A remark on minimal Lagrangian diffeomorphisms and the Monge-Ampère equation. Zbl 1158.53061
Urbas, John
2007
Interior curvature bounds for a class of curvature equations. Zbl 1174.35378
Sheng, Weimin; Urbas, John; Wang, Xu-Jia
2004
The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. Zbl 1080.53062
Urbas, John
2003
Interior curvature bounds for spacelike hypersurfaces of prescribed $$k$$-th mean curvature. Zbl 1079.53094
Urbas, John
2003
Monotonicity formulae and curvature equations. Zbl 1075.53034
Urbas, John
2003
Hessian equations on compact Riemannian manifolds. Zbl 1052.58025
Urbas, John
2002
Weingarten hypersurfaces with prescribed gradient image. Zbl 1130.35341
Urbas, John
2002
An interior second derivative bound for solutions of Hessian equations. Zbl 0986.35035
Urbas, John
2001
The second boundary value problem for a class of Hessian equations. Zbl 1194.35158
Urbas, John
2001
Some new estimates for solutions of degenerate two dimensional Monge-Ampère equations. Zbl 1158.35367
Urbas, John
2001
Some interior regularity results for solutions of Hessian equations. Zbl 0965.35056
Urbas, John
2000
An interior curvature bound for hypersurfaces of prescribed $$k$$-th mean curvature. Zbl 0959.53031
Urbas, John
2000
A note on the contact angle boundary condition for Monge-Ampère equations. Zbl 0941.35033
Urbas, John
2000
Convex curves moving homothetically by negative powers of their curvature. Zbl 0970.53039
Urbas, John
1999
Complete noncompact self-similar solutions of Gauss curvature flows. II. Negative powers. Zbl 0957.53033
Urbas, John
1999
Self-similar solutions of Gauss curvature flows. Zbl 0919.35043
Urbas, John
1999
Oblique boundary value problems for equations of Monge-Ampère type. Zbl 0912.35068
Urbas, John
1998
Complete noncompact self-similar solutions of Gauss curvature flows. I: Positive powers. Zbl 0910.53043
Urbas, John
1998
On the second boundary value problem for equations of Monge-Ampère type. Zbl 0880.35031
Urbas, John
1997
Nonlinear oblique boundary value problems for two-dimensional curvature equations. Zbl 0853.35046
Urbas, John
1996
Nonlinear oblique boundary value problems for Hessian equations in two dimensions. Zbl 0841.35042
Urbas, John
1995
Correction to: “An expansion of convex hypersurfaces”. Zbl 0777.53011
Urbas, John I. E.
1992
An expansion of convex hypersurfaces. Zbl 0746.53006
Urbas, John I. E.
1991
Boundary regularity for solutions of the equation of prescribed Gauss curvature. Zbl 0757.35024
Urbas, J. I. E.
1991
Regularity of almost extremal solutions of Monge-Ampère equations. Zbl 0735.35036
Urbas, John I. E.
1991
On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures. Zbl 0691.35048
Urbas, John I. E.
1990
On the existence of nonclassical solutions for two classes of fully nonlinear elliptic equations. Zbl 0724.35028
Urbas, John I. E.
1990
Regularity of generalized solutions of Monge-Ampère equations. Zbl 0617.35017
Urbas, John I. E.
1988
Global Hölder estimates for equations of Monge-Ampère type. Zbl 0674.35026
Urbas, John I. E.
1988
The oblique derivative problem for equations of Monge-Ampere type in two dimensions. Zbl 0649.35038
Urbas, John I. E.
1987
The Neumann problem for equations of Monge-Ampère type. Zbl 0604.35027
Lions, P.-L.; Trudinger, N. S.; Urbas, J. I. E.
1986
The generalized Dirichlet problem for equations of Monge-Ampère type. Zbl 0602.35038
Urbas, John I. E.
1986
The Neumann problem for equations of Monge-Ampère type. Zbl 0617.35050
Lions, P.-L.; Trudinger, N. S.; Urbas, J. I. E.
1986
On second derivative estimates for equations of Monge-Ampère type. Zbl 0557.35054
Trudinger, Neil S.; Urbas, John I. E.
1984
The equation of prescribed Gauss curvature without boundary conditions. Zbl 0566.53013
Urbas, John I. E.
1984
The Dirichlet problem for the equation of prescribed Gauss curvature. Zbl 0524.35047
Trudinger, Neil S.; Urbas, John I. E.
1983
all top 5

#### Cited by 367 Authors

 20 Trudinger, Neil Sidney 14 Bao, Jiguang 13 Wang, Xu-Jia 12 Tsai, Dong-Ho 11 Urbas, John Ivan Eugene 10 Jiang, Feida 9 Scheuer, Julian 9 Sheng, Weimin 7 Jian, Huai-Yu 7 Jiao, Heming 7 Li, YanYan 7 Liu, Jiakun 6 Delanoë, Philippe P. 6 Figalli, Alessio 6 Guan, Bo 6 Li, Haigang 6 Li, Qirui 6 Lu, Jian 5 Andrews, Ben 5 Dai, Limei 5 Ivaki, Mohammad N. 5 Lin, Yu-Chu 5 Liu, Yannan 5 Loeper, Grégoire 5 McCann, Robert J. 5 McCoy, James Alexander 4 Chou, Kai-Seng 4 Dong, Weisong 4 Guan, Pengfei 4 Huang, Rongli 4 Huang, Yong 4 Karakhanyan, Aram L. 3 Allen, Brian Michael 3 Ambrosio, Luigi 3 Bao, Gejun 3 Benamou, Jean-David 3 Chen, Shibing 3 Dinew, Sławomir 3 Feng, Meiqiang 3 Ivochkina, Nina Mikhaĭlovna 3 Ju, Hongjie 3 Kröner, Heiko 3 Kutev, Nikolai D. 3 Li, Dongsheng 3 Li, Guanghan 3 Li, Haizhong 3 Ma, Xi-Nan 3 Mao, Jing 3 Martino, Vittorio 3 Montanari, Annamaria 3 Poon, Chicheung 3 Sawyer, Eric T. 3 Takimoto, Kazuhiro 3 Tu, Qiang 3 Wang, Yi 3 Wei, Yong 3 Wheeden, Richard Lee 3 Xia, Chao 3 Xiang, Ni 3 Yang, Xiaoping 3 Yuan, Yu 3 Zhang, Xuemei 2 Barrett, John W. 2 Bayard, Pierre 2 Błocki, Zbigniew 2 Bryan, Paul 2 Chang, Sun-Yung Alice 2 Chen, Li 2 Chow, Bennett 2 Cui, Fan 2 Daskalopoulos, Panagiota 2 De Philippis, Guido 2 Enache, Cristian 2 Froese Hamfeldt, Brittany 2 Froese, Brittany D. 2 Garcke, Harald 2 Girão, Frederico 2 Guillen, Nestor 2 Guo, Xi 2 Hong, Jiaxing 2 Kim, Daehwan 2 Kim, Young-Heon 2 Krylov, Nicolaĭ Vladimirovich 2 Lambert, Ben 2 Lee, Ki-Ahm 2 Li, Aobing 2 Li, You 2 Li, Zhisu 2 Lopes de Lima, Levi 2 Lu, Lijiang 2 Luo, Yousong 2 Ma, Shanshan 2 Marquardt, Thomas 2 Mazzieri, Lorenzo 2 Miao, Pengzi 2 Nakamori, Saori 2 Nguyen, Luc 2 Nürnberg, Robert 2 Oberman, Adam M. 2 Otto, Felix ...and 267 more Authors
all top 5

#### Cited in 100 Serials

 43 Calculus of Variations and Partial Differential Equations 24 Journal of Differential Equations 17 Journal of Mathematical Analysis and Applications 17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 17 Proceedings of the American Mathematical Society 16 Advances in Mathematics 12 The Journal of Geometric Analysis 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Communications in Partial Differential Equations 10 Discrete and Continuous Dynamical Systems 8 Archive for Rational Mechanics and Analysis 8 Mathematische Zeitschrift 8 Transactions of the American Mathematical Society 7 Duke Mathematical Journal 7 Communications on Pure and Applied Analysis 6 Journal of Functional Analysis 6 Manuscripta Mathematica 5 Communications on Pure and Applied Mathematics 5 Journal of Computational Physics 5 Inventiones Mathematicae 5 Science China. Mathematics 4 Chinese Annals of Mathematics. Series B 4 NoDEA. Nonlinear Differential Equations and Applications 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Bulletin of Mathematical Sciences 3 Bulletin of the Australian Mathematical Society 3 Acta Mathematica 3 Archiv der Mathematik 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Annalen 3 Results in Mathematics 3 International Journal of Mathematics 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Journal of Mathematical Sciences (New York) 3 Communications in Contemporary Mathematics 3 Frontiers of Mathematics in China 2 Mathematics of Computation 2 Annales de l’Institut Fourier 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Applied Mathematics Letters 2 Science in China. Series A 2 Differential Geometry and its Applications 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 SIAM Journal on Mathematical Analysis 2 SIAM Journal on Scientific Computing 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Annales Henri Poincaré 2 Journal of Evolution Equations 2 Analysis & PDE 1 Applicable Analysis 1 Classical and Quantum Gravity 1 Communications in Mathematical Physics 1 Geophysical and Astrophysical Fluid Dynamics 1 General Relativity and Gravitation 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Nonlinearity 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of the Korean Mathematical Society 1 Mathematika 1 Pacific Journal of Mathematics 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Computer Aided Geometric Design 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of the American Mathematical Society 1 Mathematical and Computer Modelling 1 European Journal of Applied Mathematics 1 Journal of Global Optimization 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Geometric and Functional Analysis. GAFA 1 Aequationes Mathematicae 1 Elemente der Mathematik 1 Journal of Elasticity 1 Potential Analysis 1 Applied Mathematics. Series B (English Edition) 1 St. Petersburg Mathematical Journal 1 Abstract and Applied Analysis 1 Revista Matemática Complutense 1 Annals of Mathematics. Second Series 1 Analysis (München) 1 Communications in Nonlinear Science and Numerical Simulation 1 Advances in Geometry 1 Advanced Nonlinear Studies 1 Milan Journal of Mathematics 1 Complex Variables and Elliptic Equations 1 Journal of Fixed Point Theory and Applications 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Topology and Analysis 1 Communications in Mathematics and Statistics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Complex Manifolds
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#### Cited in 31 Fields

 290 Partial differential equations (35-XX) 156 Differential geometry (53-XX) 44 Global analysis, analysis on manifolds (58-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 24 Convex and discrete geometry (52-XX) 18 Numerical analysis (65-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Operations research, mathematical programming (90-XX) 6 Operator theory (47-XX) 5 Real functions (26-XX) 5 Optics, electromagnetic theory (78-XX) 4 Measure and integration (28-XX) 4 Potential theory (31-XX) 4 Ordinary differential equations (34-XX) 4 Fluid mechanics (76-XX) 4 Relativity and gravitational theory (83-XX) 4 Geophysics (86-XX) 4 Systems theory; control (93-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Geometry (51-XX) 3 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)