Inverse inclusion problem: A stable method to determine disks

In this paper we are interested in the inverse inclusion problem in the plane. We derived Hölder stability estimates for the inversion using a general single boundary measurement, and under the assumption that the inclusion has a circular shape. The Hölder power in the stability estimates only depends on the position of the target inclusion and shows that the identification is better when the inclusion is closer to the boundary. We finally proposed a simple minimizing numerical scheme for the recovery of the inclusion. Our numerical results are in good agreement with the obtained Hölder stability estimates.