Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity

Peter Hornung

doi:10.1016/j.crma.2009.03.031

Differential Geometry

Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity

Presented by: John Ball

Peter Hornung ¹

¹Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 647-650

Abstract (Original language)
Résumé

Let $S \subset R^{2}$ be a bounded $C^{\infty}$ -domain. In this Note we consider $W^{2, 2}$ isometric immersions $u : S \to R^{3}$ 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.

Soit $S \subset R^{2}$ un $C^{\infty}$ -domaine borné. Dans cette Note on considère une immersion $W^{2, 2}$ -isométrique $u : S \to R^{3}$ 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.

Received: 2008-03-13
Accepted: 2009-03-31
Published online: 2009-04-21

DOI: 10.1016/j.crma.2009.03.031

Author's affiliations:

Peter Hornung ¹

¹ Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

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Peter Hornung. Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 647-650. doi: 10.1016/j.crma.2009.03.031

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