The influence of the Hardy potential and a Convection Term on a Nonlinear Degenerate Elliptic Equations
Fessel Achhoud, Abdelkader Bouajaja, Hicham Redwane
TL;DR
This work addresses the existence of renormalized solutions for a nonlinear degenerate elliptic equation that includes both a nonlinear convection term and a Hardy-type singular potential. The authors develop a framework based on Lorentz-Marcinkiewicz spaces, construct regularized problems, and derive uniform a priori and energy estimates to control the singular Hardy term. They demonstrate a.e. convergence of the approximate gradients and pass to the limit to obtain a renormalized solution under precise parameter constraints, extending the theory to incorporate both convection and Hardy potentials in a degenerate setting. The results advance the understanding of degenerate elliptic problems with singular potentials and rough data, providing tools for handling non-coercive structures and singularities in PDEs.
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 $m\geq 1$.