Hölder stability for an inverse medium problem with internal data

Abstract

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 Holder type. For sake of simplicity, we limited our study to the class of Helmholtz equations ∆+V with bounded potential V.