Regularity for solutions of elliptic $$p(x)-$$ Laplacian type equations with lower order terms and hardy potential

Abstract

This paper aims to investigate a type of nonlinear elliptic equation that contains a Hardy potential, lower order term and \(L^{m(.)}\) datum in the setting of Sobolev spaces with variable exponent. Despite the presence of a Hardy potential, the existence of solutions and regularizing effect of some lower order terms in \(p(x)-\)Laplacian type elliptic equations are proved.