On Solutions of Elliptic Equations with Variable Exponents and Measure Data in R

Abstract

Anisotropic second-order elliptic equations with variable exponents of the nonlinearities and with right-hand side being a diffuse measure are considered in the space Rn. The existence of an entropy solution in anisotropic Sobolev–Orlicz spaces with variable exponents is proved. This entropy solution is shown to be a renormalized solution.