Error Estimates of Homogenization in the Neumann Boundary Problem for an Elliptic Equation with Multiscale Coefficients

We study the Neumann problem in a bounded domain Ω for a scalar elliptic equation with coefficients oscillating with respect to two groups of variables with periods of different smallness order. We prove the H1- and L2-estimates of homogenization. The estimates have the operator form and can be expressed in terms of the resolvent of the original problem and its approximations in the operator (L2(Ω)→H1(Ω))- and (L2(Ω)→L2(Ω))- norms.