Uniform boundary regularity in almost-periodic homogenization

In the present paper, we generalize the theory of quantitative homogenization for second-order elliptic systems with rapidly oscillating coefficients in APW2(Rd)APW2(Rd), which is the space of almost-periodic functions in the sense of H. Weyl. We obtain the large scale uniform boundary Lipschitz estimate, for both Dirichlet and Neumann problems in C1,αC1,α domains. We also obtain large scale uniform boundary Hölder estimates in C1,αC1,α domains and L2L2 Rellich estimates in Lipschitz domains.