Continuity at a boundary point of solutions to quasilinear elliptic equations with generalized Orlicz growth and non-logarithmic conditions

TL;DR

This paper investigates boundary regularity for solutions to quasilinear elliptic equations with Musielak-Orlicz growth, establishing a Wiener-type condition for boundary point regularity under non-logarithmic coefficient conditions.

Contribution

It introduces a Wiener-type criterion for boundary regularity of solutions with Musielak-Orlicz (p,q)-growth and non-logarithmic conditions, advancing understanding of boundary behavior.

Findings

Established a Wiener-type condition for boundary regularity.

Extended regularity results to Musielak-Orlicz (p,q)-growth equations.

Addressed non-logarithmic coefficient conditions.

Abstract

We consider the Dirichlet problem for quasilinear elliptic equations with Musielak-Orlicz (p,q)-growth and non-logarithmic conditions on the coefficients. A sufficient Wiener-type condition for the regularity of a boundary point is established.