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Comptes Rendus Mathématique
Volume 340, n° 1
pages 27-30 (janvier 2005)
Doi : 10.1016/j.crma.2004.11.021
Received : 12 November 2004 ;  accepted : 19 November 2004
On Poincaréʼs and J.L. Lionsʼ lemmas
Sur les lemmes de Poincaré et de J.L. Lions
 

Srinivasan Kesavan
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai - 600 113, India 

Abstract

Let be a bounded, connected and simply connected open subset of   with a Lipschitz continuous boundary. It is shown that an irrotational vector field whose components are in   is the gradient of a function in  . It is also shown that this generalization of a classical lemma of Poincaré is equivalent to a well-known lemma of J.L. Lions. To cite this article: S. Kesavan, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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Résumé

Soit un ouvert borné de   connexe et simplement connexe à frontière lipschitzienne. On montre quʼun champ vectoriel à composantes dans   dont le rotationnel est nul est le gradient dʼune fonction dans  . On montre que cette généralisation dʼun lemme classique de Poincaré est equivalent à un lemme très connu de J.L. Lions. Pour citer cet article : S. Kesavan, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.


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