Combined effects of homogenization and singular perturbations: Quantitative estimates
Combined effects of homogenization and singular perturbations: Quantitative estimates
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DOI：
10.3233/asy-211709
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发表时间：
2020-05
期刊：
影响因子：
--
通讯作者：
Weisheng Niu;Zhongwei Shen
中科院分区：
文献类型：
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作者：
Weisheng Niu;Zhongwei Shen
研究了具有奇异四阶扰动的二阶弹性椭圆系统周期均匀化的定量估计。建立了收敛速率，它取决于表示奇异扰动强度的尺度$\kappa$和非均质性的长度尺度$\epsilon$。我们也得到了大尺度的Lipschitz估计，小到$\epsilon$，独立于$\kappa$。这种大规模的估计，当与小规模的估计相结合时，产生了经典的Lipschitz估计，该估计在$\epsilon$和$\kappa$中是一致的。
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 $\kappa$.