Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems

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 Holder continuous of order $alpha$ for any $alpha in (0,1)$.