The biharmonic problem in the half-space with traces in weighted Sobolev spaces

Chérif Amrouche; Yves Raudin

doi:10.1016/j.crma.2007.03.016

Partial Differential Equations

The biharmonic problem in the half-space with traces in weighted Sobolev spaces

Presented by: Philippe G. Ciarlet

Chérif Amrouche ¹; Yves Raudin ¹

¹ Laboratoire de mathématiques appliquées, Université de Pau et des pays de l'Adour, IPRA, avenue de l'université, 64000 Pau, France

Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 553-558.

Abstract
Résumé

In this Note, we study the biharmonic equation in the half-space $R_{+}^{N}$ , with $N ⩾ 2$ . We prove in $L^{p}$ theory, with $1 < p < \infty$ , 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 $N ⩾ 2$ . Nous donnons en théorie $L^{p}$ , avec $1 < p < \infty$ , 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.

Received: 2007-02-15
Accepted: 2007-02-23
Published online: 2007-04-27

DOI: 10.1016/j.crma.2007.03.016

Author's affiliations:

Chérif Amrouche ¹; Yves Raudin ¹

¹ Laboratoire de mathématiques appliquées, Université de Pau et des pays de l'Adour, IPRA, avenue de l'université, 64000 Pau, France

@article{CRMATH_2007__344_9_553_0,
     author = {Ch\'erif Amrouche and Yves Raudin},
     title = {The biharmonic problem in the half-space with traces in weighted {Sobolev} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {553--558},
     publisher = {Elsevier},
     volume = {344},
     number = {9},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.016},
     language = {en},
}

TY  - JOUR
AU  - Chérif Amrouche
AU  - Yves Raudin
TI  - The biharmonic problem in the half-space with traces in weighted Sobolev spaces
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 553
EP  - 558
VL  - 344
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2007.03.016
LA  - en
ID  - CRMATH_2007__344_9_553_0
ER  -

%0 Journal Article
%A Chérif Amrouche
%A Yves Raudin
%T The biharmonic problem in the half-space with traces in weighted Sobolev spaces
%J Comptes Rendus. Mathématique
%D 2007
%P 553-558
%V 344
%N 9
%I Elsevier
%R 10.1016/j.crma.2007.03.016
%G en
%F CRMATH_2007__344_9_553_0

Chérif Amrouche; Yves Raudin. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.016/

References
Cited by

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

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

[3] T.Z. Boulmezaoud 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

Cited by Sources:

Comments - Policy