Combined effects of homogenization and singular perturbations: Quantitative estimates

We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale κ that represents the strength of the singular perturbation and on the length scale ϵ of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale ϵ and independent of κ. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both ϵ and κ.