Article Contents
Article Contents

# Reconstruction of the singularities of a potential from backscattering data in 2D and 3D

• We prove that the singularities of a potential in two and three dimensional Schrödinger equation are the same as those of the Born approximation (Diffraction Tomography), obtained from backscattering inverse data, with an accuracy of $1/2^-$ derivative in the scale of $L^2$-based Sobolev spaces. This improves previous results, see [30] and [20], removing several constrains on the a priori regularity of the potential. The improvement is based on the study of the smoothing properties of the quartic term in the Neumann-Born expansion of the scattering amplitude in 3D, together with a Leibniz formula for multiple scattering valid in any dimension.
Mathematics Subject Classification: Primary: 34A55, 35P25, 81U40.

 Citation:

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