Quantitative homogenization for the case of an interface between two heterogeneous media
Marc Josien and Claudia Raithel
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Submission date: 03. Dec. 2019
MSC-Numbers: 35B27, 35J15, 74A10, 74A50
Keywords and phrases: homogenization, interfaces, correctors
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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.