Unique determination of unknown boundaries in an elastic plate by one measurement

In this article we study two inverse problems for a thin elastic plate subjected to a given couple field applied at its boundary. One problem consists in determining an unknown portion of the exterior boundary of the plate subjected to homogeneous Neumann conditions, while the other problem concerns with the determination of a rigid inclusion inside the plate. In both cases, under the assumption that the plate is made by isotropic material, we prove uniqueness with one measurement