Heterogeneous time-harmonic Maxwell equations in bidimensional domains

This note deals with the low-frequency time-harmonic Maxwell equations for a heterogeneous media in bidimensional bounded domains. We propose a three step method to solve this problem. First, we construct an extension of the boundary data solving a scalar Neumann problem for the Laplace operator. Second, we solve a problem in the conductor with an unusual boundary condition of nonlocal type. Third, we solve a boundary value problem in the insulator using the solution calculated in the conductor. Also, this third problem can be reduced to a Neumann problem for the Laplace operator.