Solutions with interior bubble and boundary layer for an elliptic Neumann problem with critical nonlinearity

Juncheng Wei; Shusen Yan

doi:10.1016/j.crma.2006.07.010

Partial Differential Equations

Solutions with interior bubble and boundary layer for an elliptic Neumann problem with critical nonlinearity
[Solution explosant au centre et le long du bord pour un problème elliptique de Neumann avec non-linéarité critique]

Présenté par : Pierre-Louis Lions

Juncheng Wei ¹ ; Shusen Yan ²

¹ Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
² School of Mathematics, Statistics and Computer Science, The University of New England, Armidale, NSW 2351, Australia

Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 311-316.

Résumé
Abstract

Nous considérons le problème $ϵ^{2} Δ u - u + u^{\frac{n + 2}{n - 2}} = 0$ , $u > 0,$ dans la boule unité B de $R^{n}$ où $n = 3, 4, 5$ , $ϵ > 0$ est petit et u vérifie les conditions au bord de Neumann. Nous montrons l'existence d'une solution radiale se concentrant au centre et le long de la frontière de B quand ϵ tend vers 0.

We study positive solutions of the equation $ϵ^{2} Δ u - u + u^{\frac{n + 2}{n - 2}} = 0$ , where $n = 3, 4, 5$ and $ϵ > 0$ is small, with Neumann boundary condition in a unit ball B. We prove the existence of solutions with an interior bubble at the center and a boundary layer at the boundary ∂B.

Reçu le : 2006-03-14
Accepté le : 2006-05-17
Publié le : 2006-08-14

DOI : 10.1016/j.crma.2006.07.010

Affiliations des auteurs :

Juncheng Wei ¹ ; Shusen Yan ²

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     title = {Solutions with interior bubble and boundary layer for an elliptic {Neumann} problem with critical nonlinearity},
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     pages = {311--316},
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     language = {en},
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Juncheng Wei; Shusen Yan. Solutions with interior bubble and boundary layer for an elliptic Neumann problem with critical nonlinearity. Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 311-316. doi : 10.1016/j.crma.2006.07.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.07.010/

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