Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions
From MaRDI portal
Publication:554225
DOI10.1016/j.bulsci.2011.04.007zbMath1228.35271arXiv1012.4667OpenAlexW3099172912MaRDI QIDQ554225
Roman G. Novikov, Matteo Santacesaria
Publication date: 29 July 2011
Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1012.4667
global uniqueness and reconstructionmulti-channel Gel'fand-Calderón inverse problem in 2Dnon-overdetermined inverse problems
Inverse problems for PDEs (35R30) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items
Inverse boundary problems for systems in two dimensions ⋮ Energy- and regularity-dependent stability estimates for near-field inverse scattering in multidimensions ⋮ Uniqueness for inverse boundary value problems by Dirichlet-to-Neumann map on subboundaries ⋮ Stability estimates for recovering the potential by the impedance boundary map ⋮ Towards bulk metric reconstruction from extremal area variations ⋮ Global stability for the multi-channel Gelfand-Calderón inverse problem in two dimensions ⋮ Stability for determination of Riemannian metrics by spectral data and Dirichlet-to-Neumann map limited on arbitrary subboundary ⋮ Reconstruction and stability for piecewise smooth potentials in the plane ⋮ The Neumann-to-Dirichlet map in two dimensions ⋮ Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
- The inverse scattering problem on a fixed energy level for two- dimensional Schrödinger operator
- Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity
- A global stability estimate for the Gel'fand–Calderón inverse problem in two dimensions
- New global stability estimates for the Gel'fand–Calderon inverse problem
- Direct numerical reconstruction of conductivities in three dimensions using scattering transforms
- Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
- Stable determination of conductivity by boundary measurements
- Inverse Scattering Problem for the Schrödinger Operator with External Yang–Mills Potentials in Two Dimensions at Fixed Energy
- Recovering a potential from Cauchy data in the two-dimensional case
