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Regularity of a transmission problem and periodic homogenization
Journal de Mathématiques Pures et Appliquées ( IF 2.3 ) Pub Date : 2021-07-22 , DOI: 10.1016/j.matpur.2021.07.003
Jinping Zhuge 1
Affiliation  

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 Ck,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 C1,α interface when the coefficients on both sides of the interface are periodic with independent structures and oscillating at different microscopic scales. The proofs rely on the notion of “piecewise linear solutions” which captures the essential structure of the transmission problem.



中文翻译:

传输问题的规律性和周期性同质化

本文涉及复合材料中出现的传输问题的规律性理论。我们给出了一个新的独立证明C,α在对界面和数据的最小假设下对界面两侧的估计。此外,我们证明了一致的 Lipschitz 估计C1,α当界面两侧的系数呈周期性、结构独立且在不同的微观尺度上振荡时,界面即为界面。证明依赖于“分段线性解决方案”的概念,该概念捕获了传输问题的基本结构。

更新日期:2021-08-15
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