IUMJ

Title: Uniform regularity estimates in parabolic homogenization

Authors: Zhongwei Shen and Jun Geng

Issue: Volume 64 (2015), Issue 3, 697-733

Abstract:

We consider a family of second-order parabolic systems in divergence form with rapidly oscillating and time-dependent periodic coefficients, arising in the theory of homogenization. We obtain uniform interior $W^{1,p}$, H\"older, and Lipschitz estimates as well as boundary $W^{1,p}$ and H\"older estimates, using compactness methods. As a consequence, we establish uniform $W^{1,p}$ estimates for the initial-Dirichlet problems in $C^{1}$ cylinders.