Regularity of a transmission problem and periodic homogenization

2020/08/15 by Jinping Zhuge, Zhuge, Jinping · 1 citation
Mathematics · #35B27 #35B65 #35J47 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B27 #msc:35B65 #msc:35J47

paper · pdf · doi:10.48550/arxiv.2008.06797

This is an updated version

arxiv created 2020/08/27 · arxiv updated 2020/08/28

Abstract

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.

Cited by

• Decay Properties of Invariant Measure and Application to Elliptic Homogenization of Non-divergence Form with an Interface

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