A regularity classification of boundary points for p-harmonic functions and quasiminimizers

Abstract

In this paper it is shown that irregular boundary points for p-harmonic functions as well as for quasiminimizers can be divided into semiregular and strongly irregular points with vastly different boundary behaviour. This division is emphasized by a large number of characterizations of semiregular points. The results hold in complete metric spaces equipped with a doubling measure supporting a Poincaré inequality. They also apply to Cheeger p-harmonic functions and in the Euclidean setting to A-harmonic functions, with the usual assumptions on A.

Cite this paper

@inproceedings{Bjrn2009ARC, title={A regularity classification of boundary points for p-harmonic functions and quasiminimizers}, author={Anders Bj{\"{o}rn}, year={2009} }