no. 11-12
Differential Geometry
Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity
[Minimiseurs de la fonctionnelle de Kirchhoff : équations de Euler–Lagrange et régularité]

Présenté par : John Ball

Hornung, Peter1
1 Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Comptes Rendus. Mathématique, Tome 347 (2009) no. 11-12, pp. 647-650.

Soit S⊂R2 un C∞-domaine borné. Dans cette Note on considère une immersion W2,2-isométrique u:S→R3 qui minimise la fonctionnelle de Kirchhoff sous les conditions frontières imposant les valeurs de u et ∇u sur des partie de ∂S. On en déduit les équations de Euler–Lagrange satisfaites par u et un résultat de régularité pour u.

Let S⊂R2 be a bounded C∞-domain. In this Note we consider W2,2 isometric immersions u:S→R3 which minimize Kirchhoff's plate functional under boundary conditions prescribing the values of u and of ∇u on parts of ∂S. We derive the Euler–Lagrange equations satisfied by u and we derive regularity results for u.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.03.031
Hornung, Peter 1

1 Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany 
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Hornung, Peter. Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity. Comptes Rendus. Mathématique, Tome 347 (2009) no. 11-12, pp. 647-650. doi : 10.1016/j.crma.2009.03.031. http://www.numdam.org/articles/10.1016/j.crma.2009.03.031/

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