Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities

摘要

In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations (?△)~σ u = u~(n+2σ?2σ) with an isolated singularity, where σ ∈ (0, 1). We prove that all the solutions are asymptotically radially symmetric. When σ = 1, these have been proved by Caffarelli et al. (Comm Pure Appl Math 42:271–297, 1989).