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2011, Graduate studies in mathematics, ISBN 0821853236, Volume 121, xii, 313
"Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in... 
Minimal surfaces
Book
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2017, Volume 86, Issue 307, pp. 2159 - 2191
Journal Article
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, ISSN 0362-546X, 07/2015, Volume 121, pp. 336 - 369
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2018, Volume 264, Issue 1, pp. 341 - 377
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2019, Volume 470, Issue 2, pp. 1185 - 1193
In this paper we study the Dirichlet problem of a class of nonlinear elliptic equations which includes Monge–Ampère equation, K-Hessian equation and the usual... 
Hölder estimate | Fully nonlinear | Singular elliptic equation | MATHEMATICS | MINKOWSKI PROBLEM | MATHEMATICS, APPLIED | REGULARITY | SMOOTHNESS | Holder estirnate | MONGE-AMPERE EQUATION
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2019, Volume 343, pp. 538 - 566
We study a general class of fully nonlinear elliptic equations of second order on Hermitian manifolds. We derive a priori estimates and prove some existence... 
Hermtian manifolds | Fully nonlinear elliptic equations | A priori estimates | Mixed Chern–Ricci curvatures | Existence of solutions | 2ND-ORDER ESTIMATE | Mixed Chern-Ricci curvatures | COMPLEX MONGE-AMPERE | J-FLOW | MATHEMATICS | REGULARITY | CURVATURE | DIRICHLET PROBLEM | CONVERGENCE | MANIFOLDS
Journal Article
by Yu, Hui
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 09/2017, Volume 34, Issue 5, pp. 1141 - 1153
We prove a Wσ,ϵ-estimate for a class of nonlocal fully nonlinear elliptic equations by following Fanghua Lin's original approach [8] to the analogous problem... 
Nonlocal equations | Nonlinear elliptic equations | Potential estimate
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2020, Volume 43, Issue 1, pp. 320 - 333
In this article, we prove the Liouville‐type theorem for stable solutions of weighted p‐Laplace–type Grushin equations 1... 
Grushin operator | Liouville‐type theorem | stable solutions | p‐Laplace–type | Liouville-type theorem | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | p-Laplace-type | STABLE-SOLUTIONS | Theorems | Nonlinear equations | Elliptic functions
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 05/2020, Volume 194, p. 111445
We consider elliptic equations with measurable nonlinearities in a half cube Q2R∩{(x1,x′)∈Rn:x1>0} where the boundary data is given on Q2R∩{(x1,x′)∈Rn:x1=0}.... 
Riesz potentials | Nonlinear elliptic equations | MATHEMATICS | MATHEMATICS, APPLIED | ZYGMUND THEORY | PARABOLIC EQUATIONS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 08/2015, Volume 259, Issue 3, pp. 898 - 924
In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is.... 
Existence results | Nonlinear elliptic equations | Renormalized solutions | Neumann problems | EXISTENCE | MATHEMATICS | SYMMETRIZATION | PARABOLIC EQUATIONS | LOWER-ORDER TERMS | Analysis of PDEs | Mathematics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2019, Volume 267, Issue 9, pp. 5576 - 5600
In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove... 
Analytic periodic solutions | Anderson localization | Nash-Moser iterations | Nonlinear elliptic equations | Rectangular tori | KAM theory | SCHRODINGER-EQUATIONS | THEOREM | QUASI-PERIODIC SOLUTIONS | OSCILLATOR | MATHEMATICS | KAM | SOBOLEV NORMS | SPECTRUM | WAVE-EQUATIONS | OPERATORS
Journal Article
Nonlinear Analysis, Theory, Methods and Applications, ISSN 0362-546X, 04/2017, Volume 153, pp. 130 - 141
We consider some nonlinear Dirichlet problems and we study how lower order terms can give a regularizing effect on the solutions: the existence of... 
solutions | Nonlinear Dirichlet problem
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 12/2018, Volume 177, pp. 572 - 585
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 02/2017, Volume 147, Issue 1, pp. 25 - 60
Journal Article
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, ISSN 0362-546X, 05/2020, Volume 194
We prove an analogue of Wolff's inequality for the so-called intrinsic nonlinear potentials associated with the quasilinear elliptic equation -Delta(p)u =... 
MATHEMATICS | Wolff's inequality | MATHEMATICS, APPLIED | p-Laplacian | Nonlinear potentials | TRACE INEQUALITIES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2018, Volume 467, Issue 1, pp. 67 - 94
We prove a global Calderón–Zygmund-type estimate in the framework of Lorentz spaces for the gradients of weak solutions of nonlinear elliptic equations with... 
Lorentz estimate | Reifenberg flatness | Small bounded mean oscillation | [formula omitted]-growth | Strong log-Hölder continuity | Nonlinear elliptic problems | MATHEMATICS, APPLIED | BMO COEFFICIENTS | MATHEMATICS | L-p(center dot) log L-growth | VARIABLE EXPONENT | Strong log-Holder continuity | SYSTEMS | VMO | FUNCTIONALS
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 01/2016, Volume 22, Issue 1, pp. 289 - 308
We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is {-Delta u = f( x)/u gamma + mu... 
singular elliptic equations | measure data | Nonlinear elliptic equations | EXISTENCE | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | DIRICHLET PROBLEM | NONLINEARITIES | CONVERGENCE | AUTOMATION & CONTROL SYSTEMS | Radon | Elliptic functions | Mathematics - Analysis of PDEs
Journal Article
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