In this Note, we establish two Greenʼs formulas with little regularity on a surface. These formulas are then used for identifying and justifying Donati-like compatibility conditions on a surface, guaranteeing that the components of two symmetric matrix fields and with and in the space , where ω is a domain in , are the covariant components of the linearized change of metric and linearized change of curvature tensors associated with a displacement vector field of a surface , where is a smooth immersion.
Dans cette Note, on établit deux formules de Green avec peu de régularité sur une surface. Ces formules sont ensuite utilisées pour identifier et justifier des conditions de compatibilité du type de Donati sur une surface, garantissant que les composantes de deux champs de matrices symétriques et avec et dans lʼespace , où ω est un domaine ω de , sont les composantes covariantes des champs de tenseurs de changement de métrique et de changement de courbure linéarisés associés à un champ de déplacements dʼune surface , où est une immersion régulière.
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Philippe G. Ciarlet 1; Oana Iosifescu 2
@article{CRMATH_2013__351_21-22_853_0, author = {Philippe G. Ciarlet and Oana Iosifescu}, title = {Green's formulas with little regularity on a surface {\textendash} {Application} to {Donati-like} compatibility conditions on a surface}, journal = {Comptes Rendus. Math\'ematique}, pages = {853--858}, publisher = {Elsevier}, volume = {351}, number = {21-22}, year = {2013}, doi = {10.1016/j.crma.2013.10.016}, language = {en}, }
TY - JOUR AU - Philippe G. Ciarlet AU - Oana Iosifescu TI - Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface JO - Comptes Rendus. Mathématique PY - 2013 SP - 853 EP - 858 VL - 351 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2013.10.016 LA - en ID - CRMATH_2013__351_21-22_853_0 ER -
%0 Journal Article %A Philippe G. Ciarlet %A Oana Iosifescu %T Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface %J Comptes Rendus. Mathématique %D 2013 %P 853-858 %V 351 %N 21-22 %I Elsevier %R 10.1016/j.crma.2013.10.016 %G en %F CRMATH_2013__351_21-22_853_0
Philippe G. Ciarlet; Oana Iosifescu. Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 853-858. doi : 10.1016/j.crma.2013.10.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.016/
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