Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials

TL;DR

This paper establishes existence and regularity results for nonlinear anisotropic elliptic equations involving Hardy-type potentials and gradient-dependent lower-order terms, advancing understanding of such complex PDEs.

Contribution

It introduces new existence and regularity results for anisotropic elliptic equations with Hardy potentials and gradient dependence, extending previous theories.

Findings

Existence of solutions under broad conditions

Regularity results for solutions

Handling of Hardy-type potentials in anisotropic settings

Abstract

We give existence and regularity results for solutions of some nonlinear elliptic problems. The equations we deal with are modeled on a problem which involves in its principal part an anisotropic operator, a Hardy-type potential, and a lower-order term depending on the gradient.