# Stable Determination of the Support of Discontinuous Lamé Moduli by the Dirichlet-to-Neumann Map

Giovanni Alessandrini, Michele Di Cristo, Antonino Morassi^{*} and Edi Rosset

We consider the inverse problem of identifying an unknown inclusion compactly contained in an elastic body by boundary measurements. The body is made by linearly elastic, homogeneous and isotropic material. The Lamé moduli of the inclusion are constant and different from those of the surrounding material. In particular we study the continuous dependence of the inclusion from the Dirichlet-to-Neumann map. Under mild a priori regularity assumptions on the unknown defect, we establish a logarithmic stability estimate. Main tools of the proof are propagation of smallness arguments based on three-spheres inequality for solutions to the Lamé system and refined local approximation of the fundamental solution of the Lamé system with piecewise constant coefficients.

Mathematics Subject Classification: 35J47 35A08

Keywords: Inverse problems; inclusion; elasticity; stability; Dirichlet-to-Neumann map

Minisymposion: Inverse Problems in Elasticity