论文标题
传输问题的规律性和定期均质化
Regularity of a transmission problem and periodic homogenization
论文作者
论文摘要
本文涉及复合材料中传播问题的规律性理论。我们在界面和数据上的最小假设下，为界面两侧的$ c^{k，α} $估计提供了新的独立证明。此外，当界面两侧的系数是周期性的，具有独立的结构，并且在不同的显微镜尺度上振荡时，我们证明了$ c^{1，α} $接口的均匀Lipschitz估计值。
This paper is concerned with the regularity theory of a transmission problem arising in composite materials. We give a new self-contained proof for the $C^{k,α}$ estimates on both sides of the interface under the minimal assumptions on the interface and data. Moreover, we prove the uniform Lipschitz estimate across a $C^{1,α}$ interface when the coefficients on both sides of the interface are periodic with independent structures and oscillating at different microscopic scales.
