Uniqueness in potential scattering with reduced data

ABSTRACT

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value of the energy. We show that these data determine the bounded potential uniquely.

KEYWORDS:

• Backscattering
• inverse problem
• scattering data
• uniqueness

MATHEMATICS SUBJECT CLASSIFICATION:

• 35J10
• 35E25
• 35P25
• 35Q15
• 35R30
• 35Q53

Acknowledgments

The authors are thankful to Rakesh, Eemeli Blåsten, Uwe Kähler and Lassi Päivärinta, David Colton and Armin Lechleiter for useful discussions.