Comptes Rendus
Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layer
Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 85-90.

The Neumann problem is considered in a domain Ω, which can differ from a periodic layer inside a compact set. We prove the Fredholm property of the corresponding operator in step-weighted Sobolev spaces and determine its kernel and cokernel. All these results are based on the obtained asymptotic representation of solutions at infinity.

On considère un problème de Neumann dans un domaine Ω, qui coincide avec une couche périodique excepté sur une partie compacte. On démontre que l'opérateur correspondant satisfait à la propriété de Fredholm dans des espaces de Sobolev avec poids et on détermine son noyau et son conoyau. Tous ces résultats sont déduits de la représentation asymptotique des solutions à l'infini.

Published online:
DOI: 10.1016/S1631-0721(02)00005-0
Keywords: Computational solid mechanics, Periodic layer, Homogenization procedure, Asymptotic behaviour, Step-weighted spaces
Mot clés : Mécanique des solides numérique, Couche périodique, Processus d'homogénéisation, Comportement asymptotique, Espaces avec poids

Sergueı̈ A. Nazarov 1; Gudrun Thäter 2

1 Inst. of Mechanical Engineering Problems, V. O. Bol'shoı̈ pr. 61, St. Petersburg, 199178, Russia
2 Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
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Sergueı̈ A. Nazarov; Gudrun Thäter. Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layer. Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 85-90. doi : 10.1016/S1631-0721(02)00005-0.

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