Homogenization of the Neumann boundary value problem: polygonal domains

In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data in the convex polygonal domains. As a consequence, we obtain the pointwise and \(L^{p}\) $L^p$ convergence results. Our techniques are based on using Fourier analysis method as well as Diophantine condition on the boundary