Stable determination of the support of discontinuous Lamé moduli in an elastic body by the D-to-N map
We consider the inverse problem consisting in identifying an unknown inclusion inside an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material and contains an inclusion whose Lamé moduli are different from those of the surrounding material. Under mild a-priori regularity assumptions on the unknown defect, we establish a logarithmic stability estimate. Main tools are propagation of smallness arguments based on three-spheres inequality for solutions to the Lamé system and a refined asymptotic analysis of the fundamental solution of the Lamé system in presence of an inclusion, which shows surprising differences with the scalar conductivity case.
This is a joint work with Giovanni Alessandrini (Università di Trieste, Italy), Michele Di Cristo (Politecnico di Milano, Italy), Antonino Morassi (Università di Udine, Italy).