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Journal Articles Communications in Partial Differential Equations Year : 2019

Some quantitative homogenization results in a simple case of interface

Abstract

Following a framework initiated by Blanc, Le Bris and Lions, this article aims at obtaining quantitative homogenization results in a simple case of interface between two periodic media. By using Avellaneda and Lin’s techniques, we provide pointwise estimates for the gradient of the solution to the multiscale problem and for the associated Green function. Also we generalize the classical two-scale expansion in order to build a pointwise approximation of the gradient of the solution to the multiscale problem (up to the interface), and, adapting Kenig, Lin and Shen’s approach, we obtain convergence rates.
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Dates and versions

hal-01946297 , version 1 (05-12-2018)

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Marc Josien. Some quantitative homogenization results in a simple case of interface. Communications in Partial Differential Equations, 2019, 44 (10), pp.907-939. ⟨10.1080/03605302.2019.1610892⟩. ⟨hal-01946297⟩

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