Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves

We consider the inverse problem of determining the Lam'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse problem when the Lam'{e} parameters and the density are assumed to be piecewise constant on a given domain partition.