Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces

被引：2

作者：

Bjorn, Anders ^{[1
]}

Hansevi, Daniel ^{[1
]}

机构：

[1] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

ANALYSIS AND GEOMETRY IN METRIC SPACES | 2019年 / 7卷 / 01期

基金：

瑞典研究理事会;

关键词：

barrier; boundary regularity; Kellogg property; metric space; obstacle problem; p-harmonic function; DIRICHLET PROBLEM; MAZURKIEWICZ BOUNDARY; SOBOLEV FUNCTIONS; KELLOGG PROPERTY; POTENTIAL-THEORY; PERRON METHOD; RESPECT; QUASIMINIMIZERS; CONTINUITY;

D O I：

10.1515/agms-2019-0009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincare inequality, 1 < p < infinity. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

引用

页码：179 / 196

页数：18

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