The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications

Abstract

In this paper boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is obtained for a large class of compactifications, but also two examples when it fails are given. This study is done for complete metric spaces equipped with doubling measures supporting a p-Poincar\'e inequality, but the results are new also in unweighted Euclidean spaces.Comment: Third version: with a correction at the end (last two pages), filling in a gap in the argument. The main paper is identical to the first version. In the second version only the title changed in the metadata (it didn't correspond to the title in the paper