PWB-method and Wiener criterion for boundary regularity under generalized Orlicz growth

TL;DR

This paper extends Perron's method and Wiener's criterion to the G(·)-Laplace equation, advancing boundary regularity analysis under generalized Orlicz growth conditions.

Contribution

It introduces a generalized framework for boundary regularity using Perron and Wiener methods for G(·)-Laplace equations, broadening classical potential theory.

Findings

Extended Perron method to G(·)-Laplace equations

Generalized Wiener criterion for boundary regularity

Applicable to equations with Orlicz growth conditions

Abstract

Perron's method and Wiener's criterion have entirely solved the Dirichlet problem for the Laplace equation. Since then, this approach has attracted the attention of many mathematicians for applying these ideas in the more general equations. So, in this paper, we extend the Perron method and the Wiener criterion to the $G(\cdot)$-Laplace equation.