This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Research Article

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

Sungwon Cho1* and Mikhail Safonov2

Author Affiliations

1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

2 School of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis, MN 55455, USA

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Boundary Value Problems 2007, 2007:057928  doi:10.1155/2007/57928

The electronic version of this article is the complete one and can be found online at:

Received:16 March 2006
Revisions received:25 April 2006
Accepted:28 May 2006
Published:3 December 2006

© 2007 Cho and Safonov

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.

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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