Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities

Abstract

In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations $(-\Delta {)}^{\sigma }u=u^{\frac{n+2\sigma }{n-2\sigma }}$ with an isolated singularity, where $\sigma \in (0,1)$. We prove that all the solutions are asymptotically radially symmetric. When $\sigma =1$, these have been proved in \cite{CGS} by Caffarelli, Gidas and Spruck.

24 pages

References in corpus (2)

• A Harnack inequality for fractional Laplace equations with lower order terms
• Asymptotic behavior of solutions to the ${\sigma }_k$-Yamabe equation near isolated singularities

Cited by in corpus (2)

• On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program
• Isolated Singularities for Semilinear Elliptic Systems with Power-Law Nonlinearity