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 $κ$.

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