论文标题
拉梅系统的层电位和带有夹紧孔的穿孔弹性培养基的均匀化
Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes
论文作者
论文摘要
我们研究了定期穿孔域中的LAMé系统，并在孔的边界处夹紧域的环境中建立定量均质化结果。我们的方法基于层势，它为各种孔单元比（孔的大小与周期细胞大小之间的比率）提供了统一的证明，更重要的是，它产生了促进误差估计的天然纠正措施。一个关键的要素是针对重新验证的细胞问题的渐近分析，这是通过探索Lamé系统周期性层电位与周期趋向于无穷大的整个空间的趋势进行研究的。
We investigate Lamé systems in periodically perforated domains, and establish quantitative homogenization results in the setting where the domain is clamped at the boundary of the holes. Our method is based on layer potentials and it provides a unified proof for various regimes of hole-cell ratios (the ratio between the size of the holes and the size of the periodic cells), and, more importantly, it yields natural correctors that facilitate error estimates. A key ingredient is the asymptotic analysis for the rescaled cell problems, and this is studied by exploring the convergence of the periodic layer potentials for the Lamé system to those in the whole space when the period tends to infinity.
