A refined convergence result in homogenization of second order parabolic systems

Abstract

We derive the sharp O(ε) convergence rate in L2(0,T;Lq0(Ω)),q0=2d/(d−1) in periodic homogenization of second order parabolic systems with bounded measurable coefficients in Lipschitz cylinders. This extends the corresponding result for elliptic systems established in [20] to parabolic systems and improves the corresponding result in L2 settings derived in [7,28] for second order parabolic systems with time-dependent coefficients.