English

Nonlinear fractional elliptic problem with singular term at the boundary

Analysis of PDEs 2018-06-11 v2

Abstract

Let ΩRN\Omega\subset \mathbb{R}^N be a bounded regular domain, 0<s<10<s<1 and N>2sN>2s. We consider (P)\left\{ \begin{array}{rcll} (-\Delta)^s u &= & \frac{u^{q}}{d^{2s}} & \text{ in }\Omega , \\ u &> & 0 & \text{in }\Omega , \\ u & = & 0 & \text{ in }\mathbb{R}^N\setminus\Omega ,% \end{array}% \right. where 0<q2s10<q\le 2^*_s-1, 0<s<10<s<1 and d(x)=dist(x,Ω)d(x) = dist(x,\partial\Omega). {The main goal } of this paper is to analyze existence and non existence of solution to problem (P)(P) according to the value of ss and qq.

Keywords

Cite

@article{arxiv.1710.00388,
  title  = {Nonlinear fractional elliptic problem with singular term at the boundary},
  author = {Boumediene Abdellaoui and kheireddine Biroud and Ana Primo},
  journal= {arXiv preprint arXiv:1710.00388},
  year   = {2018}
}
R2 v1 2026-06-22T22:00:16.194Z