Holder estimates of p-harmonic extension operators

摘要

It is now a well-known fact that for 1 < p < infinity the p-hannonic functions on domains in metric measure spaces equipped with a doubling measure supporting a (1, p)-Poincare inequality are locally Holder continuous. In this note we provide a characterization of domains in such metric spaces for which p-harmonic extensions of Holder continuous boundary data are globally Holder continuous. We also provide a link between this regularity property of the domain and the uniform p-fatness of the complement of the domain. (c) 2005 Elsevier Inc. All rights reserved.