Uniform Regularity Estimates in Parabolic Homogenization

Abstract

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

35 pages

References in corpus (1)

• Convergence Rates in L^2 for Elliptic Homogenization Problems

Cited by in corpus (1)

• Uniform Lipschitz Estimates in Bumpy Half-Spaces