Determination of the potential by a fixed angle scattering data

Abstract: In this paper, we study the fixed angle scattering problems raised by Rakesh and Salo. We show that a compactly supported potential is uniquely determined by the far field pattern at a fixed angle, which is an open problem. Our method is based on a novel Carleman estimate and the ideas introduced by Bukhgeim and Klibanov on the use of Carleman estimates for inverse problems.