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

Abstract

We study the isolated singularities of functions satisfying (E) (--$\Delta$) s v$\pm$|v| p--1 v = 0 in $\Omega$\{0}, v = 0 in R N \$\Omega$, where 0 < s < 1, p > 1 and $\Omega$ 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.