Homogenisation for a statinory Maxwell system

Abstract

We study homogenization problem for the stationary Maxwell system. It is supposed that the magnetic permeability and the dielectric permittivity locally close to fast-oscillating (with respect to some small parameter) periodic functions which can change the form on rather big distances. An asymptotic behavior to solutions of the Maxwell system outside of its spectrum is obtained. We also describe asymptotic behavior of resolvent with control of the remainder in terms of some appropriate operator norms.