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

2013/09/09 by Luis Caffarelli, Tianling Jin, Yannick Sire +1 · 44 citations
Mathematics · #Complex system #Fractional Differential Equations Solutions #Gravitational singularity #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Nonlinear system #Order (exchange) #Singularity #math.AP

paper · pdf · doi:10.1007/s00205-014-0722-4

published in Archive for Rational Mechanics and Analysis 213(1), 245-268 (Springer Science+Business Media) · 24 pages

arxiv created 2013/09/09 · openalex publication_date 2014/02/18 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations (-Δ)^σu=u^{(n+2σ)/(n-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 in \citeCGS by Caffarelli, Gidas and Spruck.

Citations

• Asymptotic behavior of solutions to the σ k -Yamabe equation near isolated singularities
• Refined asymptotics for constant scalar curvature metrics with isolated singularities

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• Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results
• Qualitative analysis of positive singular solutions for a critical elliptic system in a punctured ball
• On higher-dimensional singularities for the fractional Yamabe problem: A nonlocal Mazzeo–Pacard program
• Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
• Isolated Singularities and Measure Data Problems for Semilinear Equations Driven by Stable Lévy Operators
• Isolated Singularities for Fractional Hartree Equations
• Local asymptotics for singular solutions to critical Hartree equations
• Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents

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