Partial Differential Equations
Neumann problem for a quasilinear elliptic equation in a varying domain
Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 563-568.

We investigate the Neumann problem for a nonlinear elliptic operator of Leray–Lions type in Ω(s)=Ω\F(s), s=1,2,, where Ω is a domain in Rn (n3), F(s) is a closed set located in the neighborhood of a (n1)-dimensional manifold Γ lying inside Ω. We study the asymptotic behavior of u(s) as s, 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,, où Ω est un ouvert dans Rn (n3), F(s) est un ensemble fermé situé au voisinage d'une variété differentiable Γ de dimension (n1) à l'intérieur de Ω. Nous étudions the comportement asymptotique de u(s) quand F(s) converge vers Γ dans un sens approprié.

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DOI: 10.1016/j.crma.2006.02.011
Sango, Mamadou 1

1 Department of Mathematics and Applied Mathematics, University of Pretoria/Mamelodi Campus, Pretoria 0002, South Africa
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Sango, Mamadou. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.02.011/

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