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.
|Number of pages||34|
|State||Published - 2022|
Bibliographical noteFunding Information:
W. Niu supported by the NSF of China (11971031, 11701002). Z. Shen supported in part by NSF grant DMS-1856235.
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- convergence rate
- singular perturbation
- uniform Lipschitz estimate
ASJC Scopus subject areas
- Mathematics (all)