Determination of the potential by a fixed angle scattering data

TL;DR

This paper proves that a compactly supported potential can be uniquely identified using fixed-angle scattering data, employing a novel Carleman estimate inspired by prior inverse problem techniques.

Contribution

Introduces a new Carleman estimate approach to uniquely determine potentials from fixed-angle scattering data, advancing inverse scattering theory.

Findings

Unique determination of potentials from fixed-angle data

Development of a new Carleman estimate method

Extension of inverse problem techniques

Abstract

In this paper, we show that a compactly supported potential is uniquely determined by the far field pattern at a fixed angle. Our method is based on a new Carleman estimate and the ideas introduced by Bukhgeim and Klibanov on the use of Carleman estimates for inverse problems.