On solutions of anisotropic elliptic equations with variable exponent and measure data

TL;DR

This paper investigates the existence and properties of solutions to anisotropic elliptic equations with variable exponents and measure data, establishing the link between entropy and renormalized solutions in this complex setting.

Contribution

It proves the existence of entropy solutions and their equivalence to renormalized solutions for a broad class of anisotropic elliptic equations with measure data.

Findings

Existence of entropy solutions in anisotropic Sobolev spaces with variable exponents

Entropy solutions are also renormalized solutions of the problem

Applicable to arbitrary domains with measure data

Abstract

The Dirichlet problem in arbitrary domains for a wide class of anisotropic elliptic equations of the second order with variable exponent nonlinearities and the right-hand side as a measure is considered. The existence of an entropy solution in anisotropic Sobolev spaces with variable exponents is established.It is proved that the obtained entropy solution is a renormalized solution of the considered problem.