Singularities of fractional Emden's equations via Caffarelli-Silvestre extension (2206.04353v2)

Published 9 Jun 2022 in math.AP

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.

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