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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
102/2018

Some quantitative homogenization results in a simple case of interface

Marc Josien

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.

Received:
Dec 4, 2018
Published:
Dec 6, 2018
MSC Codes:
35B
Keywords:
homogenization, Interface, Two-scale expansion

Related publications

inJournal
2019 Journal Open Access
Marc Josien

Some quantitative homogenization results in a simple case of interface

In: Communications in partial differential equations, 44 (2019) 10, pp. 907-939