Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes

Wenjia Jing Yau Mathematical Sciences Center, Tsinghua University, No. 1 Tsinghua Yuan, Beijing 100084, People’s Republic of China

Analysis of PDEs Functional Analysis mathscidoc:2206.03017

Calculus of Variations, 60, (2), 2020.11
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.
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@inproceedings{wenjia2020layer,
  title={Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes},
  author={Wenjia Jing},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626171129005035472},
  booktitle={Calculus of Variations},
  volume={60},
  number={2},
  year={2020},
}
Wenjia Jing. Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes. 2020. Vol. 60. In Calculus of Variations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626171129005035472.
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