Unique solvability of electromagnetic waves scattering by dielectric layers in weighted Sobolev space

In this paper, we study the scattering of time harmonic electromagnetic waves by a homogeneous layer above a perfectly conducting surface in weighted Sobolev space for the case of TM polarization. We first, introduce the related boundary value problem and its corresponding variational formulation. Then we establish their equivalence. Finally, we prove the problem is uniquely solvable using the results of non-weighted space case and a perturbation argument based on the commutator estimates.