Combined Effects of Homogenization and Singular Perturbations: Quantitative Estimates

26 May 2020  ·  Niu Weisheng, Shen Zhongwei ·

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 $\kappa$ that represents the strength of the singular perturbation and on the length scale $\epsilon$ of the heterogeneities, are established... We also obtain the large-scale Lipschitz estimate, down to the scale $\epsilon$ and independent of $\kappa$. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both $\epsilon$ and $\kappa$. read more

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Analysis of PDEs