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arXiv · 1905.04798

Boundary regularity for $p$-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces

Anders Björn·Daniel Hansevi
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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, $1<p<\infty$. 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.

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Anders Björn, Daniel Hansevi. 2019-05-12. Boundary regularity for $p$-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces. https://doi.org/10.1515/agms-2019-0009

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