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On non-overdetermined inverse scattering at zero energy in three dimensions

Roman Novikov
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Abstract

We develop the d-bar -approach to inverse scattering at zero energy in dimensions d>=3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential v in the Schrodinger equation from a fixed non-overdetermined ("backscattering type") restriction h on $Γ$ of the Faddeev generalized scattering amplitude h in the complex domain at zero energy in dimension d=3. For sufficiently small potentials v we formulate also a characterization theorem for the aforementioned restriction h on $Γ$ and a new characterization theorem for the full Faddeev function h in the complex domain at zero energy in dimension d=3. We show that the results of the present work have direct applications to the electrical impedance tomography via a reduction given first in [Novikov, 1987, 1988].

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Roman Novikov. 2006-05-31. On non-overdetermined inverse scattering at zero energy in three dimensions. https://arxiv.org/abs/math/0605792

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