Inverse scattering and stability for the biharmonic operator

Abstract

We investigate the inverse scattering problem of the perturbed biharmonic operator by studying the recovery process of the magnetic field A and the potential field V. We show that the high-frequency asymptotic of the scattering amplitude of the biharmonic operator uniquely determines curl A and V − 1 2 ∇ • A. We study the near-field scattering problem and show that the high-frequency asymptotic expansion up to an error O(λ −4) recovers above two quantities with no additional information about A and V. We also establish stability estimates for curl A and V − 1 2 ∇ • A.