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

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 $$W^{1,p(\cdot )}(\Omega )$$ .