Anders Björn, Daniel Hansevi
Published 2019-12-04Version 1
The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, $p$-harmonic measures, removability, and semibarriers.
Boundary regularity for $p$-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces
The Perron method associated with finely $p$-harmonic functions on finely open sets
The weak Cartan property for the p-fine topology on metric spaces
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