On considère une bande infinie avec une famille de petits trous placés le long d'une courbe. Dans ce domaine perforé, on étudie un opérateur scalaire elliptique du second ordre, avec des conditions aux limites classiques aux bords des trous. En supposant que l'emplacement des trous n'est pas périodique, on décrit les problèmes homogénéisés possibles et on démontre la convergence au sens de la norme de la résolvante des opérateurs perturbés vers les opérateurs homogénéisés. On obtient également des estimées pour le taux de convergence.
We consider an infinite strip perforated along a curve by small holes. In this perforated domain, we consider a scalar second-order elliptic differential operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic, we describe possible homogenized problems and prove the norm-resolvent convergence of the perturbed operator to a homogenized one. We also provide estimates for the rate of the convergence.
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@article{CRMATH_2014__352_9_679_0,
author = {Borisov, Denis and Cardone, Giuseppe and Durante, Tiziana},
title = {Norm-resolvent convergence for elliptic operators in domain with perforation along curve},
journal = {Comptes Rendus. Math\'ematique},
pages = {679--683},
publisher = {Elsevier},
volume = {352},
number = {9},
year = {2014},
doi = {10.1016/j.crma.2014.07.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.07.003/}
}
TY - JOUR AU - Borisov, Denis AU - Cardone, Giuseppe AU - Durante, Tiziana TI - Norm-resolvent convergence for elliptic operators in domain with perforation along curve JO - Comptes Rendus. Mathématique PY - 2014 SP - 679 EP - 683 VL - 352 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.07.003/ DO - 10.1016/j.crma.2014.07.003 LA - en ID - CRMATH_2014__352_9_679_0 ER -
%0 Journal Article %A Borisov, Denis %A Cardone, Giuseppe %A Durante, Tiziana %T Norm-resolvent convergence for elliptic operators in domain with perforation along curve %J Comptes Rendus. Mathématique %D 2014 %P 679-683 %V 352 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.07.003/ %R 10.1016/j.crma.2014.07.003 %G en %F CRMATH_2014__352_9_679_0
Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana. Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 679-683. doi : 10.1016/j.crma.2014.07.003. http://www.numdam.org/articles/10.1016/j.crma.2014.07.003/
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