Optimal Stability in the Identification of a Rigid Inclusion in an Isotropic Kirchhoff--Love Plate

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of the plate. The plate is made by nonhomogeneous, linearly elastic, and isotropic material. Under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a constructive stability estimate of log type. A key mathematical tool is a recently proved optimal three-spheres inequality at the boundary for solutions to the Kirchhoff--Love plate's equation.