Holder continuity of weak solutions of a class of linear equations with boundary degeneracy

摘要

This paper deals with a class of linear equations with boundary degeneracy. According to the degenerate ratio, the equations are divided into weakly degenerate ones and strongly degenerate ones, which should be supplemented by different Dirichlet boundary value conditions. After establishing some necessary existence, nonexistence and comparison principles, we investigate the optimal Holder continuity of weak solutions in these two cases utilizing the Harnack inequality and the Morrey theorem, respectively. (c) 2007 Elsevier Inc. All rights reserved.