The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization
Svetlana Evgenievna Pastukhova · Sbornik Mathematics · 2016
We prove an -estimate for the homogenization of an elliptic operator in a domain with a Neumann boundary condition on the boundary . The coefficients of the operator are rapidly oscillating over different groups of variables with periods of different orders of smallness as . We assume minimal regularity of the data, which makes it possible to impart to the result the meaning of an estimate in the operator -norm for the difference of the resolvents of the original and homogenized problems. We also find an approximation to the resolvent of the original problem in the operator -norm. Bibliography: 24 titles.