Partial Differential Equations
The biharmonic problem in the half-space with traces in weighted Sobolev spaces
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 553-558.

In this Note, we study the biharmonic equation in the half-space R+N, with N2. We prove in Lp theory, with 1<p<, existence, uniqueness and regularity results; then we are interested in singular boundary conditions. We consider data and give solutions which live in weighted Sobolev spaces.

Nous étudions dans cet article l'équation biharmonique dans le demi-espace R+N, avec N2. Nous donnons en théorie Lp, avec 1<p<, des résultats d'existence, d'unicité et de régularité ; nous nous intéressons ensuite à des conditions aux limites singulières. Nous considèrons des données et fournissons des solutions dans des espaces de Sobolev avec poids.

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DOI: 10.1016/j.crma.2007.03.016
Amrouche, Chérif 1; Raudin, Yves 1

1 Laboratoire de mathématiques appliquées, Université de Pau et des pays de l'Adour, IPRA, avenue de l'université, 64000 Pau, France
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Amrouche, Chérif; Raudin, Yves. The biharmonic problem in the half-space with traces in weighted Sobolev spaces. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 553-558. doi : 10.1016/j.crma.2007.03.016. http://www.numdam.org/articles/10.1016/j.crma.2007.03.016/

[1] Amrouche, C.; Girault, V.; Giroire, J. Weighted Sobolev spaces for Laplace's equation in RN, J. Math. Pures Appl., Volume 73 (1994) no. 6, pp. 579-606

[2] Amrouche, C.; Raudin, Y. Nonhomogeneous biharmonic problem in the half-space, Lp theory and generalized solutions, J. Differential Equations, Volume 236 (2007), pp. 57-81

[3] Boulmezaoud, T.Z. On the Stokes system and the biharmonic equation in the half-space: an approach via weighted Sobolev spaces, Math. Methods Appl. Sci., Volume 25 (2002), pp. 373-398

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