Homogenization of Parabolic Equations with Non-self-similar Scales

Abstract

This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as well as interior $C^{1,\alpha }$ and $C^{2,\alpha }$ estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.

40 pages