The Existence of Entropy Solutions for an Elliptic Problems Involving Variable Exponent

Abstract

In order to study the entropy solution of a class of quasilinear elliptic equations with variable exponents, first, the approximation problem of elliptic equations is established under weak operator conditions, and then the Sobolev embedding theorem, Vitali theorem and other tools are applied. The results of the existence of entropy solutions of elliptic equations are given.

Keywords

• elliptic equation
• variable exponent
• entropy solutions
• existence