度量空间中p调和函数的边界正则性及无界集上障碍问题的解

Pub Date : 2019-01-01 DOI:10.1515/agms-2019-0009

Anders Björn, Daniel Hansevi

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引用次数: 2

摘要

摘要将p-调和函数的边界正则性理论推广到完备度量空间中的无界开集，并给出了支持p-Poincaré不等式1本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.