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

Soit SR2 un C-domaine borné. Dans cette Note on considère une immersion W2,2-isométrique u:SR3 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 SR2 be a bounded C-domain. In this Note we consider W2,2 isometric immersions u:SR3 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

Peter Hornung 1

1 Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
@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},
}
TY  - JOUR
AU  - Peter Hornung
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
DO  - 10.1016/j.crma.2009.03.031
LA  - en
ID  - CRMATH_2009__347_11-12_647_0
ER  - 
%0 Journal Article
%A Peter Hornung
%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
%R 10.1016/j.crma.2009.03.031
%G en
%F CRMATH_2009__347_11-12_647_0
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/

[1] C. Bohle; G.P. Peters; U. Pinkall Constrained Willmore surfaces, Calc. Var., Volume 32 (2008), pp. 263-277

[2] G. Friesecke; R. James; S. Müller A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Comm. Pure Appl. Math., Volume 55 (2002), pp. 1461-1506

[3] P. Hornung, A density result for W2,2 isometric immersions, MIS MPG Preprint, 2007

[4] P. Hornung Approximating W2,2 isometric immersions, C. R. Acad. Sci. Paris, Ser. I, Volume 346 (2008), pp. 189-192

[5] P. Hornung, Flat minimizers of the Willmore functional: Euler–Lagrange equations, Preprint, Universität Bonn, 2008

[6] P. Hornung, Regularity results for flat minimizers of the Willmore functional, Preprint, Universität Bonn, 2008

[7] B. Kirchheim, Geometry and Rigidity of Microstructures, Habilitation thesis, University of Leipzig, 2001

[8] S. Müller; M.R. Pakzad Regularity properties of isometric immersions, Math. Z., Volume 251 (2005), pp. 313-331

[9] M.R. Pakzad On the Sobolev space of isometric immersions, J. Differential Geom., Volume 66 (2004) no. 1, pp. 47-69

[10] E.L. Starostin; G.H.M. van der Heijden The shape of a Möbius strip, Nature Materials, Volume 6 (2007), pp. 563-567

  • Peter Hornung Euler-Lagrange equation and regularity for flat minimizers of the Willmore functional, Communications on Pure and Applied Mathematics, Volume 64 (2011) no. 3, pp. 367-441 | DOI:10.1002/cpa.20342 | Zbl:1209.49061
  • A. P. Korte; E. L. Starostin; G. H. M. van der Heijden Triangular buckling patterns of twisted inextensible strips., Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, Volume 467 (2011) no. 2125, pp. 285-303 | DOI:10.1098/rspa.2010.0200 | Zbl:1219.74017
  • Peter Hornung Euler-Lagrange equations for variational problems on space curves, Physical Review E, Volume 81 (2010) no. 6 | DOI:10.1103/physreve.81.066603

Cité par 3 documents. Sources : Crossref, zbMATH

Commentaires - Politique


Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !


Publier un nouveau commentaire:

Publier une nouvelle réponse: