We consider the time-harmonic Maxwell equations set on a domain made up of two subdomains that represent a magnetic conductor and a non-magnetic material, and we assume that the relative magnetic permeability $\mu_{r}$ between the two materials is high. We prove uniform a priori estimates for Maxwell solutions when the interface between the two subdomains is supposed to be Lipschitz. Assuming smoothness for the interface between the subdomains, we prove also that the magnetic field possesses a multiscale expansion in powers of $1/ \sqrt{\mu_{r}}$ with profiles rapidly decaying inside the magnetic conductor.

翻译：我们考虑在由两个子域构成的区域上建立的时谐麦克斯韦方程组，这两个子域分别代表磁性导体和非磁性材料，并假设两种材料之间的相对磁导率 $\mu_{r}$ 很高。当两个子域之间的界面假定为 Lipschitz 连续时，我们证明了麦克斯韦解的一致先验估计。若假设子域间界面光滑，我们还证明了磁场具有以 $1/ \sqrt{\mu_{r}}$ 的幂展开的多尺度展开式，且其模态在磁性导体内部快速衰减。