Vector and scalar potentials, Poincaré's theorem and Korn's inequality

Chérif Amrouche; Philippe G. Ciarlet; Patrick Ciarlet

doi:10.1016/j.crma.2007.10.020

Partial Differential Equations

Vector and scalar potentials, Poincaré's theorem and Korn's inequality
[Potentiels vecteurs et scalaires, théorème de Poincaré et inégalité de Korn]

Présenté par : Philippe G. Ciarlet

Chérif Amrouche ¹ ; Philippe G. Ciarlet ² ; Patrick Ciarlet ³

¹ Laboratoire de mathématiques appliquées, CNRS UMR 5142, Université de Pau et des pays de l'Adour, IPRA, avenue de l'université, 64000 Pau, France
² Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
³ Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75739 Paris cedex 15, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 603-608.

Résumé
Abstract

Dans cette Note, nous présentons plusieurs résultats concernant les potentiels vecteurs et les potentiels scalaires dans des domaines bornés tridimensionnels, éventuellement multiplement connexes. En particulier, on considère des potentiels singuliers correspondant à des données dans des espaces de Sobolev d'exposant négatif. On donne également des applications au théorème de Poincaré et à l'inégalité de Korn.

In this Note, we present several results concerning vector potentials and scalar potentials in a bounded, not necessarily simply-connected, three-dimensional domain. In particular, we consider singular potentials corresponding to data in negative order Sobolev spaces. We also give some applications to Poincaré's theorem and to Korn's inequality.

Accepté le : 2007-10-06
Publié le : 2007-11-26

DOI : 10.1016/j.crma.2007.10.020

Affiliations des auteurs :

Chérif Amrouche ¹ ; Philippe G. Ciarlet ² ; Patrick Ciarlet ³

¹ Laboratoire de mathématiques appliquées, CNRS UMR 5142, Université de Pau et des pays de l'Adour, IPRA, avenue de l'université, 64000 Pau, France
² Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
³ Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75739 Paris cedex 15, France

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     author = {Ch\'erif Amrouche and Philippe G. Ciarlet and Patrick Ciarlet},
     title = {Vector and scalar potentials, {Poincar\'e's} theorem and {Korn's} inequality},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {603--608},
     publisher = {Elsevier},
     volume = {345},
     number = {11},
     year = {2007},
     doi = {10.1016/j.crma.2007.10.020},
     language = {en},
}

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Chérif Amrouche; Philippe G. Ciarlet; Patrick Ciarlet. Vector and scalar potentials, Poincaré's theorem and Korn's inequality. Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 603-608. doi : 10.1016/j.crma.2007.10.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.020/

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