Quantitative Homogenization for the Case of an Interface Between Two Heterogeneous Media

In this article we are interested in quantitative homogenization results for linear elliptic equations 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 substantially more general setting, which surrounding media may be periodic or random stationary and ergodic. Our main result is quantification sublinearity corrector adapted interface, construct using an improved version method developed by Fischer Raithel [SIAM J. Math. Anal., 49 (2017), 82--114]. optimal up logarithmic loss allows us derive almost-optimal convergence rates.