Singularities of fractional Emden's equations via Caffarelli-Silvestre extension

Huyuan Chen; Laurent Véron

paper

Singularities of fractional Emden's equations via Caffarelli-Silvestre extension

arXiv:2206.04353

Abstract

We study the isolated singularities of functions satisfying (E) (-- $Δ$ ) s v $\pm$ |v| p--1 v = 0 in $Ω$ \{0}, v = 0 in R N $Ω $, w h er e 0 < s < 1, p > 1 an d$ Ω$ is a bounded domain containing the origin. We use the Caffarelli-Silvestre extension to R + x R N. We emphasize the obtention of a priori estimates, analyse the set of self-similar solutions via energy methods to characterize the singularities.

arXiv commentJournal of Differential Equations, In press