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

Analysis and Geometry in Metric Spaces

Hansevi Daniel¹  Björn Anders¹ 

[1] Department of Mathematics, Linköping University, SE-581 83Linköping, Sweden;

关键词: barrier;    boundary regularity;    kellogg property;    metric space;    obstacle problem;    p-harmonic function;    primary: 31e05;    secondary: 30l99, 35j66, 35j92, 49q20;   

DOI  :  10.1515/agms-2019-0009

来源: DOAJ

【 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-Poincaré inequality, 1 < p < ∞. 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.

【 授权许可】

Unknown