English

On a degenerate singular elliptic problem

Analysis of PDEs 2021-09-13 v3

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 Ω\Omega is a bounded smooth domain in RN\mathbb{R}^N with N2N\geq 2, ww belong to the Muckenhoupt class ApA_p for some 1<p<1<p<\infty, ff is a nonnegative function belong to some Lebesgue space and δ>0\delta>0.

Keywords

Cite

@article{arxiv.1803.02102,
  title  = {On a degenerate singular elliptic problem},
  author = {Prashanta Garain},
  journal= {arXiv preprint arXiv:1803.02102},
  year   = {2021}
}

Comments

24 pages

R2 v1 2026-06-23T00:43:32.060Z