Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities
By Luis Caffarelli, Tianling Jin, Yannick Sire, Jingang Xiong. 2013
80 citations recorded by the source corpus.
In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations $${(-\Delta )^\sigma u=u^{\frac{n+2\sigma}{n-2\sigma}}}$$(-Δ)σu=un+2σn-2σ with an isolated singularity, where $${\sigma\in (0,1)}$$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).
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/710993f0929d97057f820822518887103d82b8ba
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In Applied Mathematics
- Tianling Jin
- Jingang Xiong
- Jun-cheng Wei
- Manuel del Pino
- Azahara DelaTorre
- María del Mar González
- Yichao Li
- Xiaoxiao Li
In Modeling and Simulation
Citations in the corpus
- Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (2019, methodology): “For σ ∈ (0, 1), this analysis has been carried out in [6].”
- Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points (2019, background): “42 (1989), no. 3, 271– 297. doi:10.1002/cpa.3160420304 [2] Caffarelli, L.; Jin, T.; Sire, Y.; Xiong, J. Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities.”
- Delaunay-type singular solutions for the fractional Yamabe problem (2015, background): “WEI In a recent paper [5] Caffarelli, Jin, Sire and Xiong characterize all the nonnegative solutions to (1.”