Comptes Rendus
no. 10
Partial differential equations
A note on the existence of extension operators for Sobolev spaces on periodic domains
[Une note sur l'existence d'opérateurs d'extension pour les espaces de Sobolev sur des domaines périodiques]

Présenté par : Olivier Pironneau

Martin Höpker1 ; Michael Böhm1
1 Center for Industrial Mathematics, FB 3, University of Bremen, Postfach 33 04 40, 28334 Bremen, Germany
Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 807-810.

Dans cette note, nous prouvons l'existence d'une famile d'opérateurs d'extension pour les espaces de Sobolev définis sur des domaines ε-périodiques. Nous montrons que les normes de ces opérateurs sont indépendantes de ε. Ce théorème est pertinent dans la théorie de l'homogénéisation des EDP avec des conditions aux limites de flux.

In this note, we prove the existence of a family of extension operators for Sobolev spaces defined on ε-periodic domains. The norms of the operators are shown to be independent of ε. This extension theorem is relevant in the theory of homogenization for PDE's under flux boundary conditions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.002
Martin Höpker 1 ; Michael Böhm 1

1 Center for Industrial Mathematics, FB 3, University of Bremen, Postfach 33 04 40, 28334 Bremen, Germany 
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Martin Höpker; Michael Böhm. A note on the existence of extension operators for Sobolev spaces on periodic domains. Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 807-810. doi : 10.1016/j.crma.2014.09.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.002/

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