On a degenerate singular elliptic problem

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^δ}\,\,\text{ in }\,\,Ω, u>0\text{ in }Ω,\\ u = 0 \text{ on } \partialΩ, \end{cases} \end{gather*} where $\hat{I}\text{c◯}$ is a bounded smooth domain in ${\mathbb{R}}^N$ with $N\ge 2$, $w$ belong to the Muckenhoupt class $A_p$ for some $1<p<\infty$, $f$ is a nonnegative function belong to some Lebesgue space and $\hat{I}´>0$.

24 pages