SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 813-854, January 2021.
In this article we are interested in quantitative homogenization results for linear elliptic equations in the nonstationary situation of a straight interface between two heterogeneous media. This extends previous work [M. Josien, Comm. Partial Differential Equations, 14 (2019), pp. 907--939] 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 by Fischer and Raithel [SIAM J. Math. Anal., 49 (2017), pp. 82--114]. This quantification is optimal up to a logarithmic loss and allows us to derive almost-optimal convergence rates.

中文翻译：

---

两个异质介质之间的界面情况下的定量均质化

SIAM数学分析杂志，第53卷，第1期，第813-854页，2021年1月。
在本文中，我们对两种异质介质之间直线界面的非平稳情况下线性椭圆方程的定量均质化结果感兴趣。这扩展了以前的工作[M. Josien，Comm。偏微分方程，14（2019），pp。907--939]到一个基本上更通用的设置，其中周围的异质介质可以是周期性的或随机的平稳的和遍历的。我们的主要结果是量化了适用于界面的均质校正器的亚线性，我们使用Fischer和Raithel [SIAM J. Math。Anal。，49（2017），第82--114页]。这种量化是最理想的，直至出现对数损失，并允许我们得出几乎最佳的收敛速度。