English

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 pp-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a pp-Poincar\'e inequality, 1<p<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, pp-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}
}