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(ε−x), 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 L 2(ℝ3)-norm with order-sharp remainder estimates.
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Dedicated to the memory of the great mathematician Mark Grigor’evich Krein
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 2, pp. 3–23, 2007
Original Russian Text Copyright © by M. Sh. Birman and T. A. Suslina
Supported by RFBR grants no. 05-01-01076-a, 05-01-02944-YaF-a.
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Birman, M.S., Suslina, T.A. Homogenization of the stationary periodic Maxwell system in the case of constant permeability. Funct Anal Its Appl 41, 81–98 (2007). https://doi.org/10.1007/s10688-007-0009-8
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DOI: https://doi.org/10.1007/s10688-007-0009-8