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 Lamé 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.