Semiregular and strongly irregular boundary points for $p$-harmonic functions on unbounded sets in metric spaces
Analysis of PDEs
2022-07-15 v1
Abstract
The trichotomy between regular, semiregular, and strongly irregular boundary points for -harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a -Poincar\'e inequality, . 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, -harmonic measures, removability, and semibarriers.
Keywords
Cite
@article{arxiv.1912.02247,
title = {Semiregular and strongly irregular boundary points for $p$-harmonic functions on unbounded sets in metric spaces},
author = {Anders Björn and Daniel Hansevi},
journal= {arXiv preprint arXiv:1912.02247},
year = {2022}
}