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 med ium 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 Frechet differentiability of the scattering map are examined. A lower bound of the linearized scatterin g map is obtained, which in particular characterizes the stability properti es. These results are useful in the analysis of the nonlinear inverse scatt ering problem. (C) 2000 Academic Press.