Boundary Value Problems

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Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains

Boundary Value Problems20062007:057928

https://doi.org/10.1155/2007/57928

©  S. Cho and M. Safonov 2007

Received: 16 March 2006

Accepted: 28 May 2006

Published: 3 December 2006

Abstract

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Michigan State University
(2)
School of Mathematics, University of Minnesota

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Copyright

© S. Cho and M. Safonov 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.