On uniqueness for an inverse problem in inhomogeneous elasticity

We consider the scattering of time-harmonic elastic waves inan isotropic medium which is characterized by constant Lamécoefficients and an inhomogeneous mass density. We prove thata knowledge of the far-field pattern for all incident planewaves and a single frequency provides sufficient informationto determine the mass density uniquely. To this end we constructa periodic Faddeev-type fundamental solution for the Navierequation and derive the existence of complex geometrical opticssolutions to the Navier equation.