Homogenization of the boundary value for the Neumann problem
Jie Zhao · Journal of Mathematical Physics · 2015
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 W1,p convergence results. Our techniques are based on Fourier analysis.