Mathematical problems in mechanics
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.

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 (cαβ) and (rαβ) with cαβ and rαβ in the space L2(ω), where ω is a domain in R2, 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 θ(ω¯), where θ:ω¯R3 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 (cαβ) et (rαβ) avec cαβ et rαβ dans lʼespace L2(ω), où ω est un domaine ω de R2, 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 θ(ω¯), où θ:ω¯R3 est une immersion régulière.

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Published online:
DOI: 10.1016/j.crma.2013.10.016
Ciarlet, Philippe G. 1; Iosifescu, Oana 2

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Départment de mathématiques, Université de Montpellier-2, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
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Ciarlet, Philippe G.; Iosifescu, Oana. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.10.016/

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