Annali di Matematica
Local behavior of solutions to fractional Hardy–Hénon
equations with isolated singularity
· Jiguang Bao
Received: 2 February 2018 / Accepted: 12 May 2018
© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer
Abstract In this paper, we study the local behaviors of positive solutions of
with an isolated singularity at the origin, where (−)
is the fractional Laplacian, 0 <σ <1,
τ>−2σ and p > 1. Our ﬁrst results provide a blowup rate estimate near an isolated
singularity, and show that the solution is asymptotically radially symmetric.
Keywords Fractional Laplacian · Isolated singularity · Rate estimate · Asymptotically
Mathematics Subject Classiﬁcation 35R11 · 35B40
The Hardy–Hénon equation
− u =|x|
has been studied in many papers, where :=
denotes the Laplacian, τ>−2,
p > 1 are parameters, the punctured unit ball B
with n ≥ 3.
The authors are supported in part by the National Natural Science Foundation of China (11631002).
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of
Education, Beijing Normal University, Beijing 100875, China