Regularity of homogenized boundary data in periodic homogenization of elliptic systems

Abstract

This paper is concerned with the 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 belongs to $W^{1,p}$ for any $1<p<\infty$. In particular, this implies that the boundary layer tails are Hölder continuous of order $\alpha$ for any $\alpha \in (0,1)$.