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

Аннотация

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.