Neumann problem for a quasilinear elliptic equation in a varying domain

Mamadou Sango

doi:10.1016/j.crma.2006.02.011

Partial Differential Equations

Neumann problem for a quasilinear elliptic equation in a varying domain

Presented by: Philippe G. Ciarlet

Mamadou Sango ¹

¹ Department of Mathematics and Applied Mathematics, University of Pretoria/Mamelodi Campus, Pretoria 0002, South Africa

Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 563-568.

Abstract
Résumé

We investigate the Neumann problem for a nonlinear elliptic operator of Leray–Lions type in $Ω^{(s)} = Ω \ F^{(s)}$ , $s = 1, 2, \dots$ , where Ω is a domain in $R^{n}$ $(n ⩾ 3)$ , $F^{(s)}$ is a closed set located in the neighborhood of a $(n - 1)$ -dimensional manifold Γ lying inside Ω. We study the asymptotic behavior of $u^{(s)}$ as $s \to \infty$ , when the set $F^{(s)}$ tends to Γ.

Nous étudions le problème de Neumann pour un opérateur élliptique de type Leray–Lions dans un domaine $Ω^{(s)} = Ω \ F^{(s)}$ , $s = 1, 2, \dots$ , où Ω est un ouvert dans $R^{n}$ $(n ⩾ 3)$ , $F^{(s)}$ est un ensemble fermé situé au voisinage d'une variété differentiable Γ de dimension $(n - 1)$ à l'intérieur de Ω. Nous étudions the comportement asymptotique de $u^{(s)}$ quand $F^{(s)}$ converge vers Γ dans un sens approprié.

Received: 2005-04-13
Accepted: 2006-02-07
Published online: 2006-03-24

DOI: 10.1016/j.crma.2006.02.011

Author's affiliations:

Mamadou Sango ¹

¹ Department of Mathematics and Applied Mathematics, University of Pretoria/Mamelodi Campus, Pretoria 0002, South Africa

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     title = {Neumann problem for a quasilinear elliptic equation in a varying domain},
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     pages = {563--568},
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     doi = {10.1016/j.crma.2006.02.011},
     language = {en},
}

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Mamadou Sango. Neumann problem for a quasilinear elliptic equation in a varying domain. Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 563-568. doi : 10.1016/j.crma.2006.02.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.011/

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