The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications
Analysis of PDEs
2020-06-05 v1
Abstract
We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron solutions. We obtain various resolutivity and invariance results, and also show that most functions that have earlier been proved to be resolutive are in fact Sobolev-resolutive. We also introduce (Sobolev)-Wiener solutions and harmonizability in this nonlinear context, and study their connections to (Sobolev)-Perron solutions, partly using Q-compactifications.
Cite
@article{arxiv.1604.08731,
title = {The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications},
author = {Anders Björn and Jana Björn and Tomas Sjödin},
journal= {arXiv preprint arXiv:1604.08731},
year = {2020}
}