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

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