On the Homogenization of the Stationary Periodic Maxwell System in a Bounded Domain

Abstract

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.