Removable singularities for sub-solutions of elliptic equations involving weighted variable exponent Sobolev spaces

TL;DR

This paper investigates conditions under which singularities in solutions to elliptic equations with weighted variable exponent Sobolev spaces can be removed, extending classical results to more general settings involving weights and variable exponents.

Contribution

It provides new sufficient conditions for the removability of singularities in elliptic equations within weighted variable exponent Sobolev spaces, generalizing previous classical results.

Findings

Established criteria for singularity removability based on generalized Minkowski content.

Extended classical elliptic regularity results to weighted variable exponent contexts.

Identified conditions on weights and exponents ensuring singularity removal.

Abstract

We study the removability of a singular set for elliptic equations involving weight functions and variable exponents. We consider the case where the singular set satisfies conditions related to some generalization of upper Minkowski content or a net measure, and give sufficient conditions for removability of this singularity for equations in the weighted variable exponent Sobolev spaces.