Hölder Stability for an Inverse Medium Problem with Internal Data

Mourad Choulli (1) , Faouzi Triki (2)

1 EDP - Equations aux dérivées partielles
2 EDP - Equations aux Dérivées Partielles

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of Hölder type. For sake of simplicity, we limited our study to the class of Helmholtz equations ∆+V with bounded potential V.

Mots clés: Helmholtz equation; inverse medium problem; internal data; Hölder stability; unique continuation

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Faouzi Triki. Hölder Stability for an Inverse Medium Problem with Internal Data. 2017. ⟨hal-01661621v1⟩