论文标题
均化和奇异扰动的综合效应：定量估计值
Combined Effects of Homogenization and Singular Perturbations: Quantitative Estimates
论文作者
论文摘要
我们研究了具有奇异四阶扰动的二阶椭圆系统的定期均质化定量估计值。建立了代表奇异扰动的强度以及异质性的长度尺度$ε$的比例$κ$的收敛速率。我们还获得了大型Lipschitz估计，直至规模$ε$，独立于$κ$。这种大规模的估计值与小规模的估计相结合，产生了古典Lipschitz估计值，在$ε$和$κ$中都均匀。
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 $κ$.
