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Báo cáo hóa học: " Research Article Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains Sungwon Cho and Mikhail Safonov"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains Sungwon Cho and Mikhail Safonov | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 57928 24 pages doi 10.1155 2007 57928 Research Article Holder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains Sungwon Cho and Mikhail Safonov Received 16 March 2006 Revised 25 April 2006 Accepted 28 May 2006 Recommended by Ugo Pietro Gianazza We establish the global Holder 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. Copyright 2007 S. Cho and M. 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. 1. Introduction In the theory of partial differential equations it is important to have estimates of solutions which do not depend on the smoothness of the given data. Such kind of estimates include different versions of the maximum principle which are crucial for investigation of boundary value problems for second-order elliptic and parabolic equations. More delicate properties of solutions such as Holder estimates and Harnack inequalities are very essential for the building of general theory of nonlinear equations see 1-6 . In this paper we establish the global Holder regularity of solutions to the Dirichlet problem or the first boundary value problem for second-order elliptic equations. We deal with the Dirichlet problem Lu f in o u 0 on do. DP Here o is a bounded open set in R n 1 satisfying the following exterior measure