In a bounded domain \(\mathscr{O}\) ⊂ ℝ³ of class C^1,1, the stationary Maxwell system with boundary conditions of perfect conductivity is considered. It is assumed that the dielectric permittivity and the magnetic permeability are given by η(x/ε) and μ(x/ε), where η and μ are symmetric bounded positive definite matrix-valued functions periodic with respect to some lattice in ℝ³. Here ε > 0 is a small parameter. It is known that, as ε > 0, the solutions of the Maxwell system weakly converge in L₂(\(\mathscr{O}\)) to the solutions of the homogenized Maxwell system with constant effective coefficients. Classical results are improved and approximations for the solutions in the L₂(\(\mathscr{O}\))-norm with error estimates of operator type are found.

中文翻译：

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有界域上平稳周期麦克斯韦系统的均质化

在一个有界域\（\ mathscr {ö} \） ⊂ℝ ³类的Ç ^1,1，固定麦克斯韦系统具有完善的电导率的边界条件被考虑。据推测，介电常数和磁导率是由下式给出η（X / ε）和μ（X / ε），其中η和μ是对称的有界正定矩阵值函数的周期性相对于在ℝ一些晶格³。此处ε > 0是一个小参数。众所周知，ε> 0时，麦克斯韦系统的解在L ₂（\（\ mathscr {O} \））中弱收敛到具有恒定有效系数的均匀麦克斯韦系统的解。改进了经典结果，并找到了L ₂（\（\ mathscr {O} \））范数中具有算符类型误差估计的解的近似值。