Inverse Scattering for Singular Potentials in Two Dimensions

DOI10.2307/2154460zbMath0787.35122OpenAlexW4230556652MaRDI QIDQ4201542

Ziqi Sun, Gunther Uhlmann

Publication date: 25 August 1993

Full work available at URL: https://doi.org/10.2307/2154460

zbMATH Keywords

potential scatteringscattering amplitudeDirichlet-to-Neumann mapobstacle scatteringtwo- dimensional Schrödinger equation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Electromagnetic theory (general) (78A25)

Related Items (6)

Inverse backscattering problem for perturbations of biharmonic operator ⋮ Uniqueness for the inverse boundary value problem with singular potentials in 2D ⋮ Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D ⋮ Inverse medium problem for a singular contrast ⋮ Reconstruction of the shape of the inclusion by boundary measurements ⋮ An \(n\)-dimensional Borg--Levinson theorem for singular potentials

Cites Work

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• A global uniqueness theorem for an inverse boundary value problem
• Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
• The inverse conductivity problem in two dimensions
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• An \(n\)-dimensional Borg-Levinson theorem
• Reconstructions from boundary measurements
• Recovery of singularities for formally determined inverse problems
• Multidimensional Inverse Scattering for First-Order Systems
• On uniqueness in th invese transmission scattering problem
• On an inverse boundary value problem in two dimensions
• A uniqueness theorem for an inverse boundary value problem in electrical prospection

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