The space $ \mathit{H}(\mathrm{div},\cdot )$ on a surface – Application to Donati-like compatibility conditions on a surface

Philippe G. Ciarlet; Oana Iosifescu

doi:10.1016/j.crma.2013.10.023

Mathematical problems in mechanics

The space

H (div, \cdot)

on a surface – Application to Donati-like compatibility conditions on a surface
[Lʼespace

H (div, \cdot)

sur une surface – Application à des conditions de compatibilité du type de Donati sur une surface]

Présenté par : Philippe G. Ciarlet

Philippe G. Ciarlet ¹ ; Oana Iosifescu 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, Volume 351 (2013) no. 23-24, pp. 943-947.

Résumé
Abstract

Dans cette Note, on montre comment définir lʼanalogue de lʼespace classique $H (div, \cdot)$ sur une surface. On établit ensuite diverses propriétés de cet espace, en particulier lʼexistence dʼune formule de Green fondamentale satisfaite par ses éléments. Ces résultats sont ensuite utilisés pour identifier des conditions de compatibilité du type de Donati sur une surface.

In this Note, we show how the analogue of the classical space $H (div, \cdot)$ can be defined on a surface. We then establish several properties of this space, notably the existence of a basic Greenʼs formula satisfied by its elements. These results are then used for identifying Donati-like compatibility conditions on a surface.

Accepté le : 2013-10-21
Publié le : 2013-11-07

DOI : 10.1016/j.crma.2013.10.023

Affiliations des auteurs :

Philippe G. Ciarlet ¹ ; Oana Iosifescu 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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     author = {Philippe G. Ciarlet and Oana Iosifescu},
     title = {The space $ \mathit{H}(\mathrm{div},\cdot )$ on a surface {\textendash} {Application} to {Donati-like} compatibility conditions on a surface},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {943--947},
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     year = {2013},
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Philippe G. Ciarlet; Oana Iosifescu. The space $ \mathit{H}(\mathrm{div},\cdot )$ on a surface – Application to Donati-like compatibility conditions on a surface. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 943-947. doi : 10.1016/j.crma.2013.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.023/

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Philippe G. Ciarlet; Oana Iosifescu Donati compatibility conditions on a surface – Application to shell theory, Journal de Mathématiques Pures et Appliquées, Volume 102 (2014) no. 1, p. 173 | DOI:10.1016/j.matpur.2013.11.006
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, p. 853 | DOI:10.1016/j.crma.2013.10.016

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