On some $\overrightarrow{p(x)}$ anisotropic elliptic equations in unbounded domain

TL;DR

This paper investigates a class of nonlinear anisotropic elliptic equations with variable exponent in unbounded domains, establishing the existence of entropy solutions without sign or coercivity constraints.

Contribution

It introduces new existence results for anisotropic elliptic problems in Sobolev spaces with variable exponents on unbounded domains, relaxing traditional conditions.

Findings

Existence of entropy solutions proven

No sign condition required for solutions

Results applicable to unbounded domains

Abstract

We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain $\Omega\subset \>I\!\!R^{N}\>(N \geq 2)\>$. We prove the existence of entropy solutions avoiding sign condition and coercivity on the lowers order terms.