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

Gang Bao, Yu Chen, Fuming Ma

Research output: Contribution to journalArticle

Abstract

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 Fréchet 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.

Original languageEnglish (US)
Pages (from-to)255-271
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume247
Issue number1
DOIs
StatePublished - Jul 1 2000

Keywords

  • Inverse scattering; Helmholtz equation; linearization; regularity; stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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