Quantitative Estimates in Reiterated Homogenization
Weisheng Niu, Zhongwei Shen, Yao Xu · arXiv (Cornell University) · 2019
This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the $L^2$ space by the reiterated homogenization method.