Uniqueness and Lipschitz stability for the identification of Lam\'e parameters from boundary measurements

In this paper we consider the problem of determining an unknown pair $\lambda$, $\mu$ of piecewise constant Lam'{e} parameters inside a three dimensional body from the Dirichlet to Neumann map. We prove uniqueness and Lipschitz continuous dependence of $\lambda$ and $\mu$ from the Dirichlet to Neumann map.