Homogenization of elliptic systems with stratified structure revisited

Abstract

We consider quantitative estimates in periodic homogenization for second-order elliptic systems with stratified structure on bounded Lipschitz domains. Under rather general smoothness assumptions on A and ρ, we establish a sharp-order scale-invariant convergence rate in $L^{2d/(d-1)}(\Omega ).$ As a byproduct, a qualitative homogenization result is also derived under more or less sharp conditions on A and ρ. The results obtained here improve our previous results greatly.