  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 $\Delta$+V with bounded potential V.
