On solutions of elliptic equations with variable exponents and measure data in ${\mathbb{R}}^n$

Abstract

Anisotropic elliptic equations of the second order with variable exponents in nonlinearities and the right-hand side as a diffuse measure are considered in the space ${\mathbb{R}}^n$. The existence of an entropy solution in anisotropic Sobolev--Orlicz spaces with variable exponents is proved. The obtained entropy solution is shown to be a renormalized solution.