Geodesic
Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 3-23

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The homogenization problem in the small period limit for the stationary periodic Maxwell system in $\mathbb{R}^3$ is considered. It is assumed that the permittivity $\eta^\varepsilon(\mathbf{x})=\eta(\varepsilon^{-1}\mathbf{x})}$, $\varepsilon>0$, is a rapidly oscillating positive matrix function and the permeability $\mu_0$ 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 $L_2(\mathbb{R}^3)$-norm with order-sharp remainder estimates.
Keywords: periodic Maxwell operator, homogenization, effective medium, corrector. 
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     author = {M. Sh. Birman and T. A. Suslina},
     title = {Homogenization of the {Stationary} {Periodic} {Maxwell} {System} in the {Case} of {Constant} {Permeability}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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M. Sh. Birman; T. A. Suslina. Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 3-23. http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a1/