Some quantitative homogenization results in a simple case of interface
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Submission date: 04. Dec. 2018
published in: Communications in partial differential equations, 44 (2019) 10, p. 907-939
DOI number (of the published article): 10.1080/03605302.2019.1610892
Keywords and phrases: homogenization, Interface, Two-scale expansion
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.