Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface

Ciarlet, Philippe G.; Iosifescu, Oana

doi:10.1016/j.crma.2013.10.016

Mathematical problems in mechanics

Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface
[Formules de Green avec peu de régularité sur une surface – Application à des conditions de compatibilité du type de Donati sur une surface]

Présenté par : Philippe G. Ciarlet

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

Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 853-858.

Résumé
Abstract

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 $(c_{α β})$ et $(r_{α β})$ avec $c_{α β}$ et $r_{α β}$ dans lʼespace $L^{2} (ω)$ , où ω est un domaine ω de $R^{2}$ , 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 $θ (\bar{ω})$ , où $θ : \bar{ω} \to R^{3}$ est une immersion régulière.

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 $(c_{α β})$ and $(r_{α β})$ with $c_{α β}$ and $r_{α β}$ in the space $L^{2} (ω)$ , where ω is a domain in $R^{2}$ , 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 $θ (\bar{ω})$ , where $θ : \bar{ω} \to R^{3}$ is a smooth immersion.

Reçu le : 2013-10-18
Publié le : 2013-10-30

DOI : 10.1016/j.crma.2013.10.016

Affiliations des auteurs :

Ciarlet, Philippe G. ¹ ; Iosifescu, Oana ²

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     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},
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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, Tome 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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