Boundary Value Problems
Volume 2007 (2007), Article ID 57928, 24 pages
Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains
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.