Let be a bounded -domain. In this Note we consider isometric immersions 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 un -domaine borné. Dans cette Note on considère une immersion -isométrique 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.
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Peter Hornung 1
@article{CRMATH_2009__347_11-12_647_0, author = {Peter Hornung}, title = {Minimizers of {Kirchhoff's} plate functional: {Euler{\textendash}Lagrange} equations and regularity}, journal = {Comptes Rendus. Math\'ematique}, pages = {647--650}, publisher = {Elsevier}, volume = {347}, number = {11-12}, year = {2009}, doi = {10.1016/j.crma.2009.03.031}, language = {en}, }
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.031/
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