H\"older Stability for an Inverse Medium Problem with Internal Data

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 H"older type. For sake of simplicity, we limited our study to the class of Helmholtz equations $\mathrm{\Delta }$+V with bounded potential V.