Localization of solutions for nonlinear elliptic problems with critical growth

Hadiji, Rejeb; Molle, Riccardo; Passaseo, Donato; Yazidi, Habib

doi:10.1016/j.crma.2006.10.018

Partial Differential Equations

Localization of solutions for nonlinear elliptic problems with critical growth
[Localisation des solutions pour un problème elliptique avec exposant critique de Sobolev]

Présenté par : Haïm Brezis

Hadiji, Rejeb ¹ ; Molle, Riccardo ² ; Passaseo, Donato ³ ; Yazidi, Habib ¹

¹ UFR des sciences et technologie, CNRS UMR 8050, université Paris 12, Val-de-Marne, 61, avenue du Général de Gaulle, 94010 Créteil, France
² Dipartimento di Matematica Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy
³ Dipartimento di Matematica “E. De Giorgi”, Università di Lecce, P.O. Box 193, 73100 Lecce, Italy

Comptes Rendus. Mathématique, Tome 343 (2006) no. 11-12, pp. 725-730.

Résumé
Abstract

On étudie l'existence et la multiplicité de solutions du problème $- div (p (x) \nabla u) = u^{2^{*} - 1} + λ u$ , $u > 0$ dans Ω et $u = 0$ sur ∂Ω dans le cas où l'ensemble de minima de p admet plusieurs composantes connexes. On s'intéresse également au cas où cet ensemble possède une seule composante connexe et une topologie complexe.

We study the existence and the multiplicity of solutions for the problem $- div (p (x) \nabla u) = u^{2^{*} - 1} + λ u$ , $u > 0$ in Ω and $u = 0$ on ∂Ω, when the set of the minimizers for the weight p has multiple connected component. We study also the case where this set has one connected component and has complex topology.

Accepté le : 2006-10-15
Publié le : 2006-11-20

DOI : 10.1016/j.crma.2006.10.018

Affiliations des auteurs :

Hadiji, Rejeb ¹ ; Molle, Riccardo ² ; Passaseo, Donato ³ ; Yazidi, Habib ¹

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     title = {Localization of solutions for nonlinear elliptic problems with critical growth},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {725--730},
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Hadiji, Rejeb; Molle, Riccardo; Passaseo, Donato; Yazidi, Habib. Localization of solutions for nonlinear elliptic problems with critical growth. Comptes Rendus. Mathématique, Tome 343 (2006) no. 11-12, pp. 725-730. doi : 10.1016/j.crma.2006.10.018. http://www.numdam.org/articles/10.1016/j.crma.2006.10.018/

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