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 .
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 .
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Philippe G. Ciarlet 1; Patrick Ciarlet 2; Giuseppe Geymonat 3; Françoise Krasucki 3
@article{CRMATH_2007__344_5_305_0, author = {Philippe G. Ciarlet and Patrick Ciarlet and Giuseppe Geymonat and Fran\c{c}oise Krasucki}, 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}, }
TY - JOUR AU - Philippe G. Ciarlet AU - Patrick Ciarlet AU - Giuseppe Geymonat AU - Françoise Krasucki 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 DO - 10.1016/j.crma.2007.01.001 LA - en ID - CRMATH_2007__344_5_305_0 ER -
%0 Journal Article %A Philippe G. Ciarlet %A Patrick Ciarlet %A Giuseppe Geymonat %A Françoise Krasucki %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 %R 10.1016/j.crma.2007.01.001 %G en %F CRMATH_2007__344_5_305_0
Philippe G. Ciarlet; Patrick Ciarlet; Giuseppe Geymonat; Françoise Krasucki. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.001/
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