Inverse inclusion problem: A stable method to determine disks

Faouzi Triki (1) , Chun-Hsiang Tsou (1)

1 EDP - Equations aux Dérivées Partielles

In this paper we are interested in inverse inclusion problem in the plane. We derive uniqueness and Hölder stability results of the inclusion recovery problem using a single boundary measurement, under the assumption that the inclusion has a circular shape. We also propose a simple minimizing scheme for the recovery of a disk. Our numerical results show that the Hölder power in the stability estimate is close to one.

Domaines: Equations aux dérivées partielles [math.AP]

Faouzi Triki, Chun-Hsiang Tsou. Inverse inclusion problem: A stable method to determine disks. Journal of Differential Equations, 2020, 259 (4), pp.3259-3281. ⟨10.1016/j.jde.2020.02.028⟩. ⟨hal-01633360⟩