Dans un domaine simplement connexe Ω de , le noyau de l'opérateur agissant sur des champs de matrices symétriques de dans , 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 .
In a simply-connected domain Ω in , the kernel of the operator acting on symmetric matrix fields from to 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 .
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@article{CRMATH_2007__344_5_305_0, author = {Ciarlet, Philippe G. and Ciarlet, Patrick Jr. and Geymonat, Giuseppe and Krasucki, Fran\c{c}oise}, title = {Characterization of the kernel of the operator {CURL\,CURL}}, journal = {Comptes Rendus. Math\'ematique}, pages = {305--308}, publisher = {Elsevier}, volume = {344}, number = {5}, year = {2007}, doi = {10.1016/j.crma.2007.01.001}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.01.001/} }
TY - JOUR AU - Ciarlet, Philippe G. AU - Ciarlet, Patrick Jr. AU - Geymonat, Giuseppe AU - Krasucki, Françoise TI - Characterization of the kernel of the operator CURL CURL JO - Comptes Rendus. Mathématique PY - 2007 SP - 305 EP - 308 VL - 344 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.01.001/ DO - 10.1016/j.crma.2007.01.001 LA - en ID - CRMATH_2007__344_5_305_0 ER -
%0 Journal Article %A Ciarlet, Philippe G. %A Ciarlet, Patrick Jr. %A Geymonat, Giuseppe %A Krasucki, Françoise %T Characterization of the kernel of the operator CURL CURL %J Comptes Rendus. Mathématique %D 2007 %P 305-308 %V 344 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.01.001/ %R 10.1016/j.crma.2007.01.001 %G en %F CRMATH_2007__344_5_305_0
Ciarlet, Philippe G.; Ciarlet, Patrick Jr.; Geymonat, Giuseppe; Krasucki, Françoise. Characterization of the kernel of the operator CURL CURL. Comptes Rendus. Mathématique, Tome 344 (2007) no. 5, pp. 305-308. doi : 10.1016/j.crma.2007.01.001. http://archive.numdam.org/articles/10.1016/j.crma.2007.01.001/
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