Abstract:

In this paper, we shall strengthen our results on the W^{1, p} 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, which gives rise to the so-called boundary layer phenomenon. Our techniques are based on integral representation of the solutions as well as analysis of oscillatory integrals, in conjunction with Fourier expansion of the oscillating periodic function.

Key words: Homogenization, Convergence rates, Oscillating, Neumann functions