Exponential instability in the Gel'fand inverse problem on the energy intervals

DOI10.1515/jiip.2011.039zbMath1279.35107arXiv1012.2193OpenAlexW2075160950MaRDI QIDQ5745468

Mikhail Isaev

Publication date: 30 January 2014

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2193

zbMATH Keywords

hyperbolic equationsDirichlet-to-Neumann mapGel'fand inverse problemstability and instability estimates

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30)

Related Items (9)

Inverse problems on low-dimensional manifolds ⋮ On instability mechanisms for inverse problems ⋮ High‐frequency stability estimates for a partial data inverse problem ⋮ Exponential instability in the inverse scattering problem on the energy interval ⋮ Stability estimates for recovering the potential by the impedance boundary map ⋮ Instability in the Gel'fand inverse problem at high energies ⋮ Global stability for the multi-channel Gelfand-Calderón inverse problem in two dimensions ⋮ CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS ⋮ Stability estimates for an inverse problem for the Schrödinger equation at negative energy in two dimensions

Cites Work

• Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
• Exponential instability in an inverse problem for the Schrödinger equation
• New global stability estimates for the Gel'fand–Calderon inverse problem
• Examples of exponential instability for inverse inclusion and scattering problems
• Stable determination of conductivity by boundary measurements
• Recovering a potential from Cauchy data in the two-dimensional case

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