Boundary Value Problems
Volume 2007 (2007), Article ID 57928, 24 pages
Research Article

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

Sungwon Cho1 and Mikhail Safonov2

1Department of Mathematics, Michigan State University, East Lansing 48824, MI, USA
2School of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis 55455, MN, USA

Received 16 March 2006; Revised 25 April 2006; Accepted 28 May 2006

Academic Editor: Ugo Pietro Gianazza

Copyright © 2007 Sungwon Cho and Mikhail 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.