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arXiv · 1912.00724

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

Marc Josien·Claudia Raithel
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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 and Raithel, 2017]. This quantification is optimal up to a logarithmic loss and allows to derive almost-optimal convergence rates.

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Marc Josien, Claudia Raithel. 2019-12-02. Quantitative homogenization for the case of an interface between two heterogeneous media. https://arxiv.org/abs/1912.00724

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