Uniqueness in inverse obstacle scattering with conductive boundary conditions

Abstract

We consider the uniqueness of the inverse obstacle scattering with conductive boundary conditions. This work is based on the original idea of Isakov for transmission boundary conditions, which utilize the solvability of the direct problem, orthogonality relations, approximations to solution of the direct problem and singular solutions. The methodology used is constructive and allows an extension to more general conditions and numerical methods.

Keywords:

• Inverse problems
• Inverse scattering
• AMS Subject Classifications: 35R30
• 35P25
• 35C15

Acknowledgments

The author thanks Victor Isakov for interesting discussions, and the referees for many helpful comments.