On Saint Venant's compatibility conditions and Poincaré's lemma

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)887-891
Journal / PublicationComptes Rendus Mathematique
Volume342
Issue number11
Publication statusPublished - 1 Jun 2006

Abstract

Saint Venant's theorem constitutes a classical characterization of smooth matrix fields as linearized strain tensor fields. This theorem has been extended to matrix fields with components in L2 by the second author and P. Ciarlet, Jr. in 2005. One objective of this Note is to further extend this characterization to matrix fields whose components are only in H-1. Another objective is to demonstrate that Saint Venant's theorem is in fact nothing but the matrix analog of Poincaré's lemma. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). © 2006 Académie des sciences.

Citation Format(s)

On Saint Venant's compatibility conditions and Poincaré's lemma. / Amrouche, Cherif; Ciarlet, Philippe G.; Gratie, Liliana et al.
In: Comptes Rendus Mathematique, Vol. 342, No. 11, 01.06.2006, p. 887-891.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review