Hölder stability for an inverse medium problem with internal data

Mourad Choulli (1) , Faouzi Triki (2)

1 IECL - Institut Élie Cartan de Lorraine
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: inverse medium problem; unique continuation; Hölder stability; Helmholtz equation; internal data

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Faouzi Triki. Hölder stability for an inverse medium problem with internal data. Research in the Mathematical Sciences , 2019, 6 (1), ⟨10.1007/s40687-018-0171-z⟩. ⟨hal-01661621v2⟩