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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
5/2020

Quantitative homogenization for the case of an interface between two heterogeneous media

Marc Josien and Claudia Raithel

Abstract

In this article we are interested in quantitative homogenization results for linear elliptic equations in the non-stationary situation of a straight interface between two heterogenous media. This extends the previous work [Josien, 2019] to a substantially more general setting, in which the surrounding heterogeneous media may be periodic or random stationary and ergodic. Our main result is a quantification of the sublinearity of a homogenization corrector adapted to the interface, which we construct using an improved version of the method developed in [Fischer & Raithel, 2017]. This quantification is optimal up to a logarithmic loss and allows to derive almost-optimal convergence rates.

Received:
Jan 9, 2020
Published:
Jan 11, 2020
MSC Codes:
35B27, 35J15, 74A10, 74A50
Keywords:
homogenization, interfaces, correctors

Related publications

inJournal
2021 Repository Open Access
Marc Josien and Claudia Raithel

Quantitative homogenization for the case of an interface between two heterogeneous media

In: SIAM journal on mathematical analysis, 53 (2021) 1, pp. 813-854