Elastic shear modulus and density profiles inversion: Lipschitz stability results

In this paper, we consider the inverse coefficients problem of recovering a shear modulus mu and density p of a medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the reconstruction of mechanical properties of tissues in non-destructive testing. We prove Lipschitz stability results for any dimension d >= 2, provided that the parameters mu and p have upper and lower bounds and belong to a known finite dimensional subspace. The proofs rely on monotonicity relations between the parameters and the Neumann-to-Dirichlet operator, combined with the techniques of localized potentials.