On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator

Nirmalendu Chaudhuri; Florica C. Cîrstea

doi:10.1016/j.crma.2008.12.018

Partial Differential Equations

On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator
[Sur la trichotomie des solutions positives singulières associées à l'opérateur de Hardy–Sobolev]

Présenté par : Haïm Brezis

Nirmalendu Chaudhuri ¹ ; Florica C. Cîrstea ²

¹ School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
² School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia

Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 153-158.

Résumé
Abstract

Dans cette Note, nous présentons une classification complète des singularités de solutions positives de l'équation $Δ u + \frac{μ}{{| x |}^{2}} u = h (u)$ dans $Ω ∖ {0}$ , où Ω est un domaine borné de $R^{N}$ , $N ⩾ 3$ , $0 \in Ω$ , et où $0 < μ < \frac{{(N - 2)}^{2}}{4}$ . Le cas $μ = 0$ avec $h (t) = t^{q}$ , $q > 1$ a été traité par Brezis et Véron.

In this Note, we present a complete classification of singularities of positive solutions of the equation $Δ u + \frac{μ}{{| x |}^{2}} u = h (u)$ in $Ω ∖ {0}$ , where Ω is a bounded domain of $R^{N}$ , $N ⩾ 3$ , $0 \in Ω$ , and $0 < μ < \frac{{(N - 2)}^{2}}{4}$ . The case $μ = 0$ with $h (t) = t^{q}$ , $q > 1$ were treated by Brezis and Véron.

Reçu le : 2008-10-16
Accepté le : 2008-12-17
Publié le : 2009-02-01

DOI : 10.1016/j.crma.2008.12.018

Affiliations des auteurs :

Nirmalendu Chaudhuri ¹ ; Florica C. Cîrstea ²

¹ School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
² School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia

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     author = {Nirmalendu Chaudhuri and Florica C. C{\^\i}rstea},
     title = {On trichotomy of positive singular solutions associated with the {Hardy{\textendash}Sobolev} operator},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {153--158},
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     volume = {347},
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     year = {2009},
     doi = {10.1016/j.crma.2008.12.018},
     language = {en},
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Nirmalendu Chaudhuri; Florica C. Cîrstea. On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 153-158. doi : 10.1016/j.crma.2008.12.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.018/

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Cité par Sources :

^☆ This work were partially supported by an Australian Research Council Grant of Professors Neil Trudinger and Xu-Jia Wang.

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