Convergence rates in homogenization of parabolic systems with locally periodic coefficients

Abstract

In this paper we study the quantitative homogenization of second-order parabolic systems with locally periodic (in both space and time) coefficients. The $O(\epsilon )$ scale-invariant error estimate in $L^2(0,T;L^{\frac{2d}{d-1}}(\Omega ))$ is established in $C^{1,1}$ cylinders under minimum smoothness conditions on the coefficients. This process relies on critical estimates of smoothing operators. We also develop a new construction of flux correctors in the parabolic manner and a sharp estimate for temporal boundary layers.

arXiv comment31 pages