The Kellogg property under generalized growth conditions

TL;DR

This paper investigates the Kellogg property for minimizers of the Dirichlet phi-energy integral under generalized Orlicz growth, establishing new results for irregular and boundary points.

Contribution

It proves the Kellogg property and characterizations of boundary points for generalized Orlicz growth, including special cases like double phase and Orlicz growth.

Findings

Set of irregular points has zero capacity

Characterizations of semiregular boundary points

Results extend known cases to more general growth conditions

Abstract

We study minimizers of the Dirichlet phi-energy integral with generalized Orlicz growth. We prove the Kellogg property, the set of irregular points has zero capacity, and give characterizations of semiregular boundary points. The results are new ever for the special cases double phase and Orlicz growth.