Variable exponent Sobolev trace spaces and Dirichlet problem in axiomatic nonlinear potential theory

TL;DR

This paper characterizes variable exponent Sobolev trace spaces and constructs a nonlinear harmonic Perron-Weiner-Brelot operator, providing conditions for its injectivity within nonlinear potential theory.

Contribution

It introduces a new characterization of variable exponent Sobolev trace spaces and develops a Perron-Weiner-Brelot operator with injectivity conditions in nonlinear harmonic spaces.

Findings

New characterization of variable exponent Sobolev trace spaces

Construction of Perron-Weiner-Brelot operator in nonlinear harmonic space

Sufficient conditions for operator injectivity

Abstract

We give a news characterization of variable exponent Sobolev trace spaces. We construct The Perron-Weiner-Brelot operator in nonlinear harmonic space and we give sufficient condition for which this operator is injective.