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

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