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Local profiles and elliptic problems at different scales with defects

Abstract : We present a possible approach to approximate at both the coarse and fine scales the solution to an elliptic equation with oscillatory coefficient when this coefficient consists of a “nice”, say periodic, function that is locally perturbed. The approach is based on a local profile, solution to an equation similar to the corrector equation in classical homogenization. The well-posedness of that equation is explored, in various functional settings depending upon the locality of the perturbation. Some related problems are discussed.
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https://hal.archives-ouvertes.fr/hal-01143311
Contributor : Xavier Blanc <>
Submitted on : Friday, April 17, 2015 - 4:42:02 PM
Last modification on : Thursday, January 7, 2021 - 4:00:05 PM
Long-term archiving on: : Monday, September 14, 2015 - 10:15:24 AM

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Xavier Blanc, Claude Le Bris, Pierre Louis Lions. Local profiles and elliptic problems at different scales with defects. Comptes Rendus Mathématique, Elsevier Masson, 2015, pp.203-208. ⟨10.1016/j.crma.2015.01.003⟩. ⟨hal-01143311⟩

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