Semiregular and strongly irregular boundary points for $p$-harmonic functions on unbounded sets in metric spaces

Abstract

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 $p$-Poincaré 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.

References in corpus (5)

• The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces
• The Perron method for $p$-harmonic functions in unbounded sets in ${\mathbf{R}}^n$ and metric spaces
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• Boundary regularity for $p$-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces