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

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dc.creatorNovikov, Roman
dc.date2006-05-31
dc.date.accessioned2026-07-07T07:48:11Z
dc.date.available2026-07-07T07:48:11Z
dc.descriptionWe 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].
dc.identifierhttps://arxiv.org/abs/math/0605792
dc.identifierhttp://arxiv.org/abs/math/0605792
dc.identifierAnnali della Scuola Normale Superiore di Pisa, Classe di Scienze 5 (2006) 279-328
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124407
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleOn non-overdetermined inverse scattering at zero energy in three dimensions
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