Holder estimates of p-harmonic extension operators

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:220

Article

Aikawa, H ; Shanmugalingam, N

关键词: Holder continuity;    harmonic extension;    p-harmonic;    metric measure space;    p-capacity;    uniformly fat;    uniformly perfect;   

DOI  :  10.1016/j.jde.2005.01.010

来源: Elsevier

【 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.

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