The influence of the Hardy potential and a Convection Term on a Nonlinear Degenerate Elliptic Equations

TL;DR

This paper establishes the existence of renormalized solutions for a class of nonlinear degenerate elliptic equations that include Hardy potentials and convection terms, under certain growth and integrability conditions.

Contribution

It introduces new existence results for nonlinear degenerate elliptic equations with Hardy potential and convection terms, expanding the understanding of such complex PDEs.

Findings

Existence of renormalized solutions proven

Applicable to equations with Hardy potential and convection

Results hold for right-hand side in L^m, m ≥ 1

Abstract

This paper is devoted to prove existence of renormalized solutions for a class of non--linear degenerate elliptic equations involving a non--linear convection term, which satisfies a growth properties, and a Hardy potential. Additionally, we assume that the right-hand side is an $L^m$ function, with $m\geq 1$.