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

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