Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem

The main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map or scattering matrix.which maps the scatterer to the scattered field. Properties on continuity and Fr´echet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties. These results are useful in the analysis of the nonlinear inverse scattering problem