Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces-Reference-Cited by-同舟云学术

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

Published:2019-01-01 Issue:1 Volume:7 Page:179-196
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:
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Author:

Björn Anders,Hansevi Daniel

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2019-0009/pdf

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