Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains
نویسندگان
چکیده
We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equations in domains satisfying an exterior cone condition, similar results were obtained by J. H. Michael, who in turn relied on the barrier techniques due to K. Miller. Our approach is based on special growth lemmas, and it works for both divergence and nondivergence, elliptic and parabolic equations, in domains satisfying a general “exterior measure” condition.
منابع مشابه
Compactness Methods for Hölder Estimates of Certain Degenerate Elliptic Equations
In this paper we obtain the interior C regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local L estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method.
متن کاملOptimal Control of Elliptic Equations with Pointwise Constraints on the Gradient of the State in Nonsmooth Polygonal Domains
This article is concerned with optimal control problems subject to a second order elliptic PDE and additional pointwise constraints on the gradient of the state. In particular, existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed. In this situation the solution operator for the partial differential equation does not provide enough regularity to state the pointwise con...
متن کاملTornado Solutions for Semilinear Elliptic Equations in R: Regularity
We give conditions under which bounded solutions to semilinear elliptic equations ∆u = f(u) on domains of R are continuous despite a possible infinite singularity of f(u). The conditions do not require a minimization or variational stability property for the solutions. The results are used in a second paper to show regularity for a familiar class of equations.
متن کاملA Meyers type regularity result for approximations of second order elliptic operators by Galerkin schemes
We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by Galerkin methods. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic operators on rather general graphs are also obtained.
متن کاملSecond Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian Manifolds
We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under structure conditions which are close to optimal. We treat both equations on closed manifolds, and the Dirichlet problem on manifolds with boundary without any geometric restrictions to the boundary. These estimates yield regularity and existence results some of ...
متن کامل