An inhomogeneous p-laplacian equation with a Hardy potential

TL;DR

This paper investigates the existence and regularity of solutions to a p-Laplacian equation with Hardy potential and inhomogeneous terms, expanding understanding of such nonlinear PDEs with singular potentials.

Contribution

It provides new results on the existence and regularity of solutions for a class of inhomogeneous p-Laplacian equations involving Hardy potentials.

Findings

Existence of solutions under certain conditions.

Regularity properties of solutions established.

Analysis of the impact of the Hardy potential on solution behavior.

Abstract

In this work we study the existence and regularity of solutions to the following equation: $$-\Delta_p u + g(x) u = \frac{\lambda}{|x|^{p}} |u|^{p-2}u + f,$$ where $1< p < N$ and $f\in L^m$, where $m\ge 1$.