Comptes Rendus
no. 23-24
Partial Differential Equations/Mathematical Problems in Mechanics
A periodic unfolding operator on certain compact Riemannian manifolds
[Un opérateur dʼéclatement périodique pour quelques variétés riemanniennes compactes]

Présenté par : Evariste Sanchez-Palencia

Sören Dobberschütz1 ; Michael Böhm2
1 Nano-Science Center, University of Kopenhagen, Universitetsparken 5, 2100 København Ø, Denmark
2 Center for Industrial Mathematics, FB 3, University of Bremen, Postfach 330 440, 28334 Bremen, Germany
Comptes Rendus. Mathématique, Volume 350 (2012) no. 23-24, pp. 1027-1030.

On propose une généralisation de la méthode dʼéclatement périodique qui peut être appliquée aux structures définies sur quelques variétés riemanniennes compactes. Tandis que la pluspart des résultats connus de lʼ éclatement périodique dans un domain en Rn est également valide, on a besoin dʼun opérateur de transport pour lʼéclatement des gradients.

In this note, we present a generalisation of the method of periodic unfolding, which can be applied to structures defined on certain compact Riemannian manifolds. While many results known from unfolding in domains of Rn can be recovered, for the unfolding of gradients a transport operator has to be defined.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.11.001
Sören Dobberschütz 1 ; Michael Böhm 2

1 Nano-Science Center, University of Kopenhagen, Universitetsparken 5, 2100 København Ø, Denmark
2 Center for Industrial Mathematics, FB 3, University of Bremen, Postfach 330 440, 28334 Bremen, Germany 
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Sören Dobberschütz; Michael Böhm. A periodic unfolding operator on certain compact Riemannian manifolds. Comptes Rendus. Mathématique, Volume 350 (2012) no. 23-24, pp. 1027-1030. doi : 10.1016/j.crma.2012.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.11.001/

[1] I. Agricola; T. Friedrich Global Analysis, AMS, Providence, RI, 2002

[2] H. Amann; J. Escher Analysis III, Birkhäuser, Basel, Switzerland, 2009

[3] D. Cioranescu; A. Damlamian; G. Griso Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 99-104

[4] D. Cioranescu; A. Damlamian; G. Griso The periodic unfolding method in homogenization, SIAM J. Math. Anal., Volume 40 (2008), pp. 1585-1620

[5] A. Damlamian An elementary introduction to periodic unfolding, GAKUTO Internat. Ser. Math. Sci. Appl., Volume 24 (2005), pp. 119-136

[6] S. Dobberschütz, Homogenization techniques for lower dimensional structures, PhD thesis, University of Bremen, http://nbn-resolving.de/urn:nbn:de:gbv:46-00102769-13.

[7] N. Neuss; M. Neuss-Radu; A. Mikelić Effective laws for the Poisson equation on domains with curved oscillating boundaries, Appl. Anal., Volume 85 (2006), pp. 479-502

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