Low Frequency Scattering Theory for a Penetrable Body with an Impenetrable Core

We consider convergent low frequency expansions of the scattering problem for a penetrable body with an impenetrable core; the core can be soft, rigid or resistive. The exterior field is represented in terms of a volume and a surface integral; this representation contains explicitly all the physical and geometrical parameters of the problem. The wave problem is reduced to a sequence of elliptic boundary value problems which can be solved iteratively using methods of potential theory.