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arXiv · 1309.2021

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

Luis Caffarelli·Tianling Jin·Yannick Sire·Jingang Xiong
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Abstract

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

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Luis Caffarelli, Tianling Jin, Yannick Sire, Jingang Xiong. 2013-09-09. Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. https://doi.org/10.1007/s00205-014-0722-4

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