Quantitative Homogenization for the Case of an Interface Between Two Heterogeneous Media
Marc Josien, Claudia Raithel · SIAM Journal on Mathematical Analysis · 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.