In this paper, we study the local behavior of nonnegative solutions of fractional semi-linear equations with an isolated singularity, where and . 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 , this classification result has been proved by Gidas and Spruck (1981) , Caffarelli et al. (1989) .
Cite this article
Hui Yang, Wenming Zou, On isolated singularities of fractional semi-linear elliptic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 2, pp. 403–420DOI 10.1016/J.ANIHPC.2020.07.003