Uniqueness for entropy solution to a class of nonlinear degenerate weighted elliptic p(.)-Laplacian problem with L1-data

Abstract

In the present paper, we prove the uniqueness of entropy solution to a class of nonlinear degenerate weighted elliptic p(·)-Laplacian problems. These particular problems are delineated by Dirichlet-type boundary conditions and L1 data. We use a priori estimates in the framework of weighted variable exponent Sobolev spaces theory.