# Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity

Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity In this paper, we study the local behaviors of positive solutions of \begin{aligned} (-\Delta )^\sigma u=|x|^{\tau }u^p \end{aligned} ( - Δ ) σ u = | x | τ u p with an isolated singularity at the origin, where $$(-\Delta )^\sigma$$ ( - Δ ) σ is the fractional Laplacian, $$0<\sigma <1$$ 0 < σ < 1 , $$\tau >-2\sigma$$ τ > - 2 σ and $$p>1$$ p > 1 . Our first results provide a blowup rate estimate near an isolated singularity, and show that the solution is asymptotically radially symmetric. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annali di Matematica Pura ed Applicata (1923 -) Springer Journals

# Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity

Annali di Matematica Pura ed Applicata (1923 -), Volume 198 (1) – May 28, 2018
19 pages

/lp/springer_journal/local-behavior-of-solutions-to-fractional-hardy-h-non-equations-with-0IehE838I2
Publisher
Springer Journals
Copyright © 2018 by Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0373-3114
eISSN
1618-1891
D.O.I.
10.1007/s10231-018-0761-9
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we study the local behaviors of positive solutions of \begin{aligned} (-\Delta )^\sigma u=|x|^{\tau }u^p \end{aligned} ( - Δ ) σ u = | x | τ u p with an isolated singularity at the origin, where $$(-\Delta )^\sigma$$ ( - Δ ) σ is the fractional Laplacian, $$0<\sigma <1$$ 0 < σ < 1 , $$\tau >-2\sigma$$ τ > - 2 σ and $$p>1$$ p > 1 . Our first results provide a blowup rate estimate near an isolated singularity, and show that the solution is asymptotically radially symmetric.

### Journal

Annali di Matematica Pura ed Applicata (1923 -)Springer Journals

Published: May 28, 2018

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