Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform

DOI10.1215/S0012-7094-01-10837-5zbMath1013.35085arXivmath/0001099OpenAlexW2039338234MaRDI QIDQ1847850

Allan Greenleaf, Gunther Uhlmann

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0001099

zbMATH Keywords

Schrödinger equationlocal uniquenessDirichlet-Neumann mapsdetermination of the potential

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Radon transform (44A12) Schrödinger operator, Schrödinger equation (35J10)

Related Items (13)

Hyperbolic geometry and local Dirichlet-Neumann map ⋮ Propagation and recovery of singularities in the inverse conductivity problem ⋮ Maxwell's equations with a polarization independent wave velocity: direct and inverse problems ⋮ An inverse boundary value problem for certain anisotropic quasilinear elliptic equations ⋮ Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets ⋮ Uniqueness in Calderón's problem with Lipschitz conductivities ⋮ The Calderón inverse problem for isotropic quasilinear conductivities ⋮ Inverse problems: seeing the unseen ⋮ Calderóns' Inverse Problem for Anisotropic Conductivity in the Plane ⋮ Determining a potential of the parabolic equation from partial boundary measurements ^* ⋮ Lipschitz stability for the inverse conductivity problem ⋮ A density property for tensor products of gradients of harmonic functions and applications ⋮ 30 years of Calderón's problem

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• A uniqueness theorem for an inverse boundary value problem in electrical prospection
• Inverse boundary value problems at the boundary—continuous dependence
• Stable determination of conductivity by boundary measurements
• Inverse problems for partial differential equations

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