2025/05/08 by Meftahi, Houcine, Nssibi, Chayma · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2505.05116
In this study, we address the inverse problem of recovering the Lamé parameters (λ, μ) and the density ρ of a medium from the Neumann-to-Dirichlet map for any dimension d≥ 2. This inverse problem finds its motivation in the reconstruction of mechanical properties of tissues in medical diagnostics. We first assume that the Lamé parameters (λ, μ) are know and we look for the inverse problem of recovering the density ρ. In this context, we derive a constrcutive Lipschitz stability estimate in terms of the Neumann to Dirichlet map in the case of piecewise constant parameters. Then, we look for the inverse problem of recovering λ, μ and ρ simultameousely. We establish Lipschitz stability estimate, provided that the parameters λ, μ and ρ have upper and lower bounds and belong to a known finite-dimensional subspace. The proofs hinge on monotonicity relations between the parameters and the Neumann-to-Dirichlet operator, coupled with the techniques of localized potentials.