Regularity of homogenized boundary data in periodic homogenization of elliptic systems

Source 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) .