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

Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity Annali di Matematica https://doi.org/10.1007/s10231-018-0761-9 Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity 1 1 Yimei Li · 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 Nature 2018 Abstract In this paper, we study the local behaviors of positive solutions of σ τ p (−) u =|x | u 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 radially symmetric Mathematics Subject Classification 35R11 · 35B40 1 Introduction The Hardy–Hénon equation τ p − u =|x | u in B \{0} (1) n ∂ has been studied in many papers, where  := denotes the Laplacian, τ> −2, i =1 ∂x p > 1 are parameters, the punctured unit ball B \{0}⊂ R with n ≥ 3. The authors are supported in part by the National Natural Science Foundation of China (11631002). Jiguang 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

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Publisher
Springer Journals
Copyright
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

Annali di Matematica https://doi.org/10.1007/s10231-018-0761-9 Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity 1 1 Yimei Li · 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 Nature 2018 Abstract In this paper, we study the local behaviors of positive solutions of σ τ p (−) u =|x | u 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 radially symmetric Mathematics Subject Classification 35R11 · 35B40 1 Introduction The Hardy–Hénon equation τ p − u =|x | u in B \{0} (1) n ∂ has been studied in many papers, where  := denotes the Laplacian, τ> −2, i =1 ∂x p > 1 are parameters, the punctured unit ball B \{0}⊂ R with n ≥ 3. The authors are supported in part by the National Natural Science Foundation of China (11631002). Jiguang

Journal

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

Published: May 28, 2018

References

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