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Summary: Analysis of the Scattering Map of a Linearized Inverse Medium
Problem for Electromagnetic Waves
Habib Ammari
Centre de Mathematiques Appliquees, CNRS UMR 7641,
Ecole Polytechnique
91128 Palaiseau, France
Gang Bao
Department of Mathematics
Michigan State University
East Lansing, MI 48824, USA
Abstract
The main goal of this paper is to study the linearization of an inverse medium
problem for Maxwell's equations. Regularity and stability results are established
for the near- eld scattering map which maps the scatterer to the scattered eld.
Properties on continuity and Frechet di erentiability of the scattering map are
examined. A lower bound of the linearized scattering map is obtained, which
in particular characterizes the stability properties of the scattering map. These
results are useful in the analysis and computation of the nonlinear inverse scattering
problem for Maxwell's equations.
Key words. Inverse scattering, Maxwell's equations, linearization, regularity, stability
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