A regularity classification of boundary points for p-harmonic functions and quasiminimizers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:338

Article

Bjorn, Anders

关键词: A-harmonic;    dirichlet problem;    doubling measure;    irregular point;    metric space;    nonlinear;    p-harmonic;    Poincare inequality;    quasiharmonic;    quasiminimizer;    semiregular;    strongly irregular;   

DOI  :  10.1016/j.jmaa.2007.04.068

来源: Elsevier

【 摘 要 】

In this paper it is shown that irregular boundary points for p-harmonic functions as well as for quasiminimizers can be divided into semiregular and strongly irregular points with vastly different boundary behaviour. This division is emphasized by a large number of characterizations of semiregular points. The results hold in complete metric spaces equipped with a doubling measure supporting a Poincare inequality. They also apply to Cheeger p-harmonic functions and in the Euclidean setting to A-harmonic functions, with the usual assumptions on A. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free