Removable singularities for Hölder continuous quasiregular mappings in the plane [PDF]
arXiv, 2006 We give necessary conditions for a set E to be removable for Holder continuous quasiregular mappings in the plane. We also obtain some removability results for Holder continuous mappings of finite distortion.
arxiv
Justification of the limiting absorption principle in R2 [PDF]
arXiv, 1999 The limiting absorption principle in two-dimensional space is justified for a second-order elliptic operators. Necessary and sufficient conditions for the right-hand side are given for this principle to be valid.
arxiv
Hölder regularity for non divergence form elliptic equations with discontinuous coefficients [PDF]
arXiv, 2012 In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.
arxiv
Lipschitz Interior regularity for the viscosity and weak solutions of the pseudo-$p$Laplacian [PDF]
arXiv, 2014 We prove interior Lipschitz regularity result for weak and viscosity solutions of the pseudo $p$Laplacien $(p-1)\sum_i |\partial_i u|^{p-2} \partial_{ii} u = f$ for $p>2$ and $f$ bounded.
arxiv
Carleman Estimate for Surface in Euclidean Space at Infinity [PDF]
arXiv, 2017 This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads to rigidity results in geometry.
arxiv
On the uniqueness of a solution to a stationary convection-diffusion equation with a generalized divergence-free drift [PDF]
arXiv, 2017 In this paper we establish the uniqueness of a solution to a stationary convection-diffusion equation in divergence form with an exponentially summable generalized divergence-free drift.
arxiv
On the exterior Dirichlet problem for special Lagrangian equations [PDF]
arXiv, 2017 In this paper, we establish the existence and uniqueness theorem of the exterior Dirichlet problem for special Lagrangian equations with prescribed asymptotic behavior at infinity.
arxiv
Liouville Type Theorems for Minimal Surface Equations in Half Space [PDF]
arXiv, 2019 For $n\geq2,$ we obtain Liouville type theorems for minimal surface equations in half space $\mathbf R^n_+$ with affine Dirichlet boundary value or constant Neumann boundary value.
arxiv
A Note on Lipschitz Continuiy of the Solutions of a Class of Elliptic Free Boundary Problems [PDF]
arXiv, 2019 We provide a new and simple proof based on Harnack's inequality to the Lipschitz continuity of the solutions of a class of free boundary problems.
arxiv
Non linear elliptic theory and the Monge-Ampere equation [PDF]
Proceedings of the ICM, Beijing 2002, vol. 1, 179--187, 2002 The Monge-Ampere equation, plays a central role in the theory of fully non linear equations. In fact we will like to show how the Monge-Ampere equation, links in some way the ideas comming from the calculus of variations and those of the theory of fully non linear equations.
arxiv