Some quantitative homogenization results in a simple case of interface

Marc Josien

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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
Bibtex
MSC-Numbers: 35B
Keywords and phrases: homogenization, Interface, Two-scale expansion

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.