Homogenization of the boundary value for the Neumann problem

In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data. Such a problem raised due to its importance for higher order approximation in homogenization theory. High order approximation gives rise to the so-called boundary layer phenomenon. As a consequence, we obtain the pointwise and W-1,W-p convergence results. Our techniques are based on Fourier analysis. (C) 2015 AIP Publishing LLC.