Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability

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.