On a degenerate singular elliptic problem

Prashanta Garain

Mathematische Nachrichten, 2022, vol. 295, issue 7, 1354-1377

Abstract: In this article we provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose prototype is given by −div(w(x)|∇u|p−2∇u)=f(x)uδinΩ,u>0inΩ,u=0on∂Ω,\begin{equation*}\hskip7pc \left\{ \def\eqcellsep{&}\begin{array}{l} -{\operatorname{div}}\big (w(x)|\nabla u|^{p-2}\nabla u\big )=\dfrac{f(x)}{u^\delta }\,\,\text{ in }\,\,\Omega ,\\[0pt] u>0\text{ in }\Omega ,\\ u = 0 \text{ on } \partial \Omega , \end{array} \right.\hskip-7pc \end{equation*}where Ω is a bounded smooth domain in RN$\mathbb {R}^N$ with N≥2$N\ge 2$, w belongs to the Muckenhoupt class Ap$A_p$ for some 1 0$\delta >0$.

Date: 2022
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