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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712, USA

    Luis Caffarelli

  2. Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL, 60637, USA

    Tianling Jin

  3. Université Aix-Marseille and LATP, 9, rue F. Joliot Curie, 13453, Marseille Cedex 13, France

    Yannick Sire

  4. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Jingang Xiong

Authors
  1. Luis Caffarelli
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  2. Tianling Jin
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  3. Yannick Sire
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  4. Jingang Xiong
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Corresponding author

Correspondence to Yannick Sire.

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Communicated by F. Lin

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Caffarelli, L., Jin, T., Sire, Y. et al. Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities. Arch Rational Mech Anal 213, 245–268 (2014). https://doi.org/10.1007/s00205-014-0722-4

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  • DOI: https://doi.org/10.1007/s00205-014-0722-4

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