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

DOI10.3934/ipi.2012.6.321zbMath1253.81129arXiv0902.3096OpenAlexW2963807960MaRDI QIDQ435844

Alberto Ruiz, Juan Manuel Reyes

Publication date: 12 July 2012

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.3096

zbMATH Keywords

inverse problemsSchrödinger equationBorn approximationinverse backscattering

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) (n)-body potential quantum scattering theory (81U10) Inverse scattering problems in quantum theory (81U40) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (8)

A Born approximation from backscattering data for live loads in Lamé system ⋮ Recovery of the singularities of a potential from backscattering data in general dimension ⋮ The double dispersion operator in backscattering: Hölder estimates and optimal Sobolev estimates for radial potentials ⋮ Fixed Angle Scattering: Recovery of Singularities and Its Limitations ⋮ The fixed angle scattering problem and wave equation inverse problems with two measurements ⋮ Inverse scattering for a random potential ⋮ Born approximation for the magnetic Schrödinger operator ⋮ Inverse backscattering Born approximation for the magnetic Schrödinger equation in three dimensions

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