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Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities |
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| Authors: | Luis Caffarelli Tianling Jin Yannick Sire Jingang Xiong |
| Institution: | 1. Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712, USA 2. Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL, 60637, USA 3. Université Aix-Marseille and LATP, 9, rue F. Joliot Curie, 13453, Marseille Cedex 13, France 4. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China |
| 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 σ = 1, these have been proved by Caffarelli et al. (Comm Pure Appl Math 42:271–297, 1989). |
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