On removable singularities for solutions of Neumann problem for elliptic equations involving variable exponent

TL;DR

This paper investigates conditions under which boundary singularities can be removed for solutions to elliptic equations with variable exponents in the Neumann problem, focusing on compact singular sets and variable exponent Sobolev spaces.

Contribution

It provides new sufficient conditions for the removability of boundary singularities in elliptic equations with variable exponents, extending previous results to this more general setting.

Findings

Sufficient conditions for boundary singularity removability.

Extension of classical results to variable exponent Sobolev spaces.

Analysis of compact singular sets in the boundary context.

Abstract

We study the removability of a singular set in the boundary of Neumann problem for elliptic equations with variable exponent. We consider the case where the singular set is compact, and give sufficient conditions for removability of this singularity for equations in the variable exponent Sobolev space.