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Journal Articles Asymptotic Analysis Year : 2020

Precised approximations in elliptic homogenization beyond the periodic setting

Xavier Blanc
Marc Josien
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  • IdHAL : marcjosien

Abstract

We consider homogenization problems for linear elliptic equations in divergence form. The coecients are assumed to be a local perturbation of some periodic background. We prove $W^{1,p}$ and Lipschitz convergence of the two-scale expansion, with explicit rates. For this purpose, we use a corrector adapted to this particular setting, and dened in [10, 11], and apply the same strategy of proof as Avellaneda and Lin in [1]. We also propose an abstract setting generalizing our particular assumptions for which the same estimates hold.
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Dates and versions

hal-01958207 , version 1 (17-12-2018)

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Xavier Blanc, Marc Josien, Claude Le Bris. Precised approximations in elliptic homogenization beyond the periodic setting. Asymptotic Analysis, 2020, 116 (2), pp.93-137. ⟨10.3233/ASY-191537⟩. ⟨hal-01958207⟩
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