Functional Analysis and Its Applications

, Volume 41, Issue 2, pp 81–98

Homogenization of the stationary periodic Maxwell system in the case of constant permeability

Authors

  • M. Sh. Birman
    • Department of PhysicsSt. Petersburg State University
  • T. A. Suslina
    • Department of PhysicsSt. Petersburg State University
Article

DOI: 10.1007/s10688-007-0009-8

Cite this article as:
Birman, M.S. & Suslina, T.A. Funct Anal Its Appl (2007) 41: 81. doi:10.1007/s10688-007-0009-8
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Abstract

The homogenization problem in the small period limit for the stationary periodic Maxwell system in ℝ3 is considered. It is assumed that the permittivity ηε(x)=η(εx), ε > 0, is a rapidly oscillating positive matrix function and the permeability µ0 is a constant positive matrix. For all four physical fields (the electric and magnetic field intensities, the electric displacement field, and the magnetic flux density), we obtain uniform approximations in the L2(ℝ3)-norm with order-sharp remainder estimates.

Key words

periodic Maxwell operatorhomogenizationeffective mediumcorrector

Copyright information

© Springer Science+Business Media, Inc. 2007