# On a degenerate singular elliptic problem

## TL;DR

This paper establishes existence, uniqueness, and regularity of solutions for a class of degenerate singular elliptic boundary value problems involving weighted p-Laplacian operators.

## Contribution

It provides new mathematical results on the well-posedness and regularity of solutions for a broad class of degenerate singular elliptic equations with weights in the Muckenhoupt class.

## Key findings

- Existence of solutions under given conditions.
- Uniqueness of solutions for the problem.
- Regularity results for solutions.

## Abstract

In this article we provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose prototype is given by \begin{gather*} \begin{cases} -\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla u)=\frac{f(x)}{u^\delta}\,\,\text{ in }\,\,\Omega, u>0\text{ in }\Omega,\\ u = 0 \text{ on } \partial\Omega, \end{cases} \end{gather*} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$ with $N\geq 2$, $w$ belong to the Muckenhoupt class $A_p$ for some $1<p<\infty$, $f$ is a nonnegative function belong to some Lebesgue space and $\delta>0$.