On isolated singularities of fractional semi-linear elliptic equations
Yang, Hui1 ; Zou, Wenming2
1 a Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
2 b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 403-420.
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In this paper, we study the local behavior of nonnegative solutions of fractional semi-linear equations (−Δ)σu=up with an isolated singularity, where σ∈(0,1) and nn−2σ<p<n+2σn−2σ. We first use the blow up method and a Liouville type theorem to derive an upper bound. Then we establish a monotonicity formula and a sufficient condition for removable singularity to give a classification of the isolated singularities. When σ=1, this classification result has been proved by Gidas and Spruck (1981) [23], Caffarelli et al. (1989) [7].

Reçu le :
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.07.003
Classification : 35B09, 35B40, 35J70, 35R11
Mots-clés : Isolated singularities, Monotonicity formula, Positive solutions, Fractional semi-linear elliptic equations
Yang, Hui 1 ; Zou, Wenming 2

1 a Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
2 b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 
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Yang, Hui; Zou, Wenming. On isolated singularities of fractional semi-linear elliptic equations. Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 403-420. doi : 10.1016/j.anihpc.2020.07.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.07.003/

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This work was supported by NSFC (11771234, 11926323).