no. 23-24
Mathematical problems in mechanics
The space H(div,⋅) on a surface – Application to Donati-like compatibility conditions on a surface
[Lʼespace H(div,⋅) 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, Oana2
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. 23-24, pp. 943-947.

Dans cette Note, on montre comment définir lʼanalogue de lʼespace classique H(div,⋅) 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,⋅) 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 :
Publié le :
DOI : 10.1016/j.crma.2013.10.023
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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     title = {The space $ \mathit{H}(\mathrm{div},\cdot )$ on a surface {\textendash} {Application} to {Donati-like} compatibility conditions on a surface},
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Ciarlet, Philippe G.; Iosifescu, Oana. The space $ \mathit{H}(\mathrm{div},\cdot )$ on a surface – Application to Donati-like compatibility conditions on a surface. Comptes Rendus. Mathématique, Tome 351 (2013) no. 23-24, pp. 943-947. doi : 10.1016/j.crma.2013.10.023. http://www.numdam.org/articles/10.1016/j.crma.2013.10.023/

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