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

Presented by: Haïm Brezis

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

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

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

Abstract (Original language)
Résumé

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.

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.

Accepted: 2006-10-15
Published online: 2006-11-20

DOI: 10.1016/j.crma.2006.10.018

Author's affiliations:

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

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     title = {Localization of solutions for nonlinear elliptic problems with critical growth},
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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, Volume 343 (2006) no. 11-12, pp. 725-730. doi: 10.1016/j.crma.2006.10.018

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