Quantitative homogenization for the case of an interface between two heterogeneous media
Analysis of PDEs
2019-12-03 v1
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.
Cite
@article{arxiv.1912.00724,
title = {Quantitative homogenization for the case of an interface between two heterogeneous media},
author = {Marc Josien and Claudia Raithel},
journal= {arXiv preprint arXiv:1912.00724},
year = {2019}
}
Comments
58 pages, 5 Figures