Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems

Zhongwei Shen; Jinping Zhuge

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arXiv · 1707.03160

Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems

Zhongwei Shen·Jinping Zhuge

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Abstract

This paper is concerned with periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belong to $W^{1, p}$ for any $1<p<\infty$. In particular, this implies that the boundary layer tails are Hölder continuous of order $α$ for any $α\in (0,1)$.

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Zhongwei Shen, Jinping Zhuge. 2017-07-11. Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems. https://arxiv.org/abs/1707.03160

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