Remarks on Neumann boundary value problems with variable exponents

Abstract

We are interested in elliptic problems with Neumann boundary conditions that are studied in the framework of isotropic and anisotropic spaces with variable exponents. We establish the existence and a unique result concerning a problem with a general p(·) - Laplace type operator. In addition, we present connections to other results, some of them involving the same operator, some of them involving a general p(·) - Laplace type operator.