Partial Differential Equations
New characterization of the kernel of the n-dimensional Laplace operator in exterior domains
Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1257-1260.

In this Note, we study the characterization of the kernel of the Laplace operator with Dirichlet boundary conditions in exterior domains. We consider data in weighted Sobolev spaces.

Nous étudions dans cette Note la caractérisation du noyau de l'opérateur laplacien avec des conditions de Dirichlet au bord dans un ouvert extérieur. Nous considérons des données dans des espaces de Sobolev avec poids.

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DOI: 10.1016/j.crma.2008.10.015
Amrouche, Chérif 1; Huy Hoang Nguyen 1

1 Laboratoire de mathématiques appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA, avenue de l'Université, 64013 Pau, France
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Amrouche, Chérif; Huy Hoang Nguyen. New characterization of the kernel of the n-dimensional Laplace operator in exterior domains. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1257-1260. doi : 10.1016/j.crma.2008.10.015. http://www.numdam.org/articles/10.1016/j.crma.2008.10.015/

[1] Adams, R.A. Sobolev Spaces, Academic Press, New York, 2003

[2] Amrouche, C.; Girault, V.; Giroire, J. Weighted Sobolev spaces for the Laplace equation in Rn, Journal de Mathématiques Pures et Appliquées, Volume 73 (1994) no. 6, pp. 579-606

[3] Amrouche, C.; Girault, V.; Giroire, J. Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: an approach in weighted Sobolev spaces, Journal de Mathématiques Pures et Appliquées, Volume 76 (1997) no. 1, pp. 55-81

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