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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@article{CRMATH_2009__347_11-12_647_0, author = {Hornung, Peter}, 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}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.031/} }
TY - JOUR AU - Hornung, Peter TI - Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity JO - Comptes Rendus. Mathématique PY - 2009 SP - 647 EP - 650 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.031/ DO - 10.1016/j.crma.2009.03.031 LA - en ID - CRMATH_2009__347_11-12_647_0 ER -
%0 Journal Article %A Hornung, Peter %T Minimizers of Kirchhoff's plate functional: Euler–Lagrange equations and regularity %J Comptes Rendus. Mathématique %D 2009 %P 647-650 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.031/ %R 10.1016/j.crma.2009.03.031 %G en %F CRMATH_2009__347_11-12_647_0
Hornung, Peter. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.03.031/
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