An approximation theorem in inverse electromagnetic scattering

In the inverse electromagnetic scattering problem for an inhomogeneity of compact support with constant permittivity Colton and Päivärinta suggested an optimization scheme which yields a numerical method for determining the refractive index if the far‐field data of the scattering problem is known [1]. We prove the denseness of the Cauchy data to certain interior transmission problems and conclude that the infimum of the optimization scheme is zero even if the permittivity varies. Before proving the denseness result, we investigate a boundary value problem which is needed to prove the denseness result.