Functional Analysis/Mathematical Problems in Mechanics
Characterization of the kernel of the operator CURL CURL
Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 305-308.

In a simply-connected domain Ω in R3, the kernel of the operator CURLCURL acting on symmetric matrix fields from Ls2(Ω) to Hs−2(Ω) coincides with the space of linearized strain tensor fields. For not simply-connected domains, Volterra has characterized this kernel for smooth fields. Here we extend this result for domains with a Lipschitz-continuous boundary for fields in Ls2(Ω).

Dans un domaine simplement connexe Ω de R3, le noyau de l'opérateur CURLCURL agissant sur des champs de matrices symétriques de Ls2(Ω) dans Hs−2(Ω), coïncide avec l'espace des champs de tenseurs de déformation linéarisés. Dans le cas de domaines non simplement connexes, Volterra a caractérisé ce noyau pour des champs réguliers. Dans cette Note, nous étendons ce résultat pour un domaine à frontière lipschitzienne et pour des champs dans Ls2(Ω).

Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.001
Ciarlet, Philippe G. 1; Ciarlet, Patrick Jr. 2; Geymonat, Giuseppe 3; Krasucki, Françoise 3

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75739 Paris cedex 15, France
3 Laboratoire de mécanique et de génie civil, UMR 5508, Université Montpellier II, place Eugène-Bataillon, 34695 Montpellier cedex 5, France
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Ciarlet, Philippe G.; Ciarlet, Patrick Jr.; Geymonat, Giuseppe; Krasucki, Françoise. Characterization of the kernel of the operator CURL CURL. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 305-308. doi : 10.1016/j.crma.2007.01.001. http://www.numdam.org/articles/10.1016/j.crma.2007.01.001/

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