On uniqueness for an inverse problem in inhomogeneous elasticity

We consider the scattering of time-harmonic elastic waves in an isotropic medium which is characterized by constant Lame coefficients and an inhomogeneous mass density. We prove that a knowledge of the far-field pattern for all incident plane waves and a single frequency provides sufficient information to determine the mass density uniquely. To this end we construct a periodic Faddeev-type fundamental solution for the Navier equation and derive the existence of complex geometrical optics solutions to the Navier equation.