scholarly journals Periodic homogenization of elliptic systems with stratified structure

2019 ◽  
Vol 39 (4) ◽  
pp. 2295-2323 ◽  
Author(s):  
Yao Xu ◽  
◽  
Weisheng Niu ◽  
Keyword(s):  
Elliptic Systems ◽  
Periodic Homogenization ◽  
Stratified Structure

scholarly journals Combined effects of homogenization and singular perturbations: Quantitative estimates

2021 ◽  
pp. 1-34
Author(s):  
Weisheng Niu ◽  
Zhongwei Shen
Keyword(s):  
Large Scale ◽  
Convergence Rates ◽  
Elliptic Systems ◽  
Small Scale ◽  
Length Scale ◽  
Combined Effects ◽  
Periodic Homogenization ◽  
Quantitative Estimates ◽  
Lipschitz Estimate ◽  
Scale Estimate

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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