Refined instability estimates for some inverse problems
From MaRDI portal
Publication:2697344
DOI10.3934/ipi.2022017OpenAlexW4226407539MaRDI QIDQ2697344
Publication date: 18 April 2023
Published in: Inverse Problems and Imaging (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/ipi.2022017
instabilityinverse problemsHelmholtz equationscattering theoryelectrical impedance tomographyCalderón's problemRellich lemmadepth-dependent instability of exponential-typeincreasing stability phenomena
Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Second-order elliptic equations (35J15)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Subspaces of stability in the Cauchy problem for the Helmholtz equation
- Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics
- A global uniqueness theorem for an inverse boundary value problem
- Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map
- A note on the existence and uniqueness of solutions of frequency domain elastic wave problems: a priori estimates in \(H^1\)
- Reconstruction of inclusions in an elastic body
- Global uniqueness for a two-dimensional inverse boundary value problem
- Partial differential equations. 2: Qualitative studies of linear equations
- Refined stability estimates in electrical impedance tomography with multi-layer structure
- On an inverse boundary value problem
- Depth dependent resolution in electrical impedance tomography
- Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit
- Exponential instability in an inverse problem for the Schrödinger equation
- Increased stability in the continuation of solutions to the Helmholtz equation
- Increasing stability for near field from the scattering amplitude
- Continuous dependence on data for solutions of partial differential equations with a prescribed bound
- Increasing stability of the inverse boundary value problem for the Schr\"odinger equation
- Reconstructing Discontinuities Using Complex Geometrical Optics Solutions
- Increasing stability of the continuation for the Maxwell system
- On uniqueness of recovery of a discontinuous conductivity coefficient
- Examples of exponential instability for inverse inclusion and scattering problems
- Stable determination of conductivity by boundary measurements
- Increasing stability in an inverse problem for the acoustic equation
- Optimality of Increasing Stability for an Inverse Boundary Value Problem
- On instability mechanisms for inverse problems
- A depth-dependent stability estimate in electrical impedance tomography
- Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit
- Inverse Problems for the Stationary Transport Equation in the Diffusion Scaling
- Optimal Depth-Dependent Distinguishability Bounds for Electrical Impedance Tomography in Arbitrary Dimension
- Linearized Inverse Schrödinger Potential Problem at a Large Wavenumber
- Inverse Acoustic and Electromagnetic Scattering Theory
- Probing for electrical inclusions with complex spherical waves
- Distinguishability Revisited: Depth Dependent Bounds on Reconstruction Quality in Electrical Impedance Tomography
- Stable Determination of an Inclusion by Boundary Measurements
- On increased stability in the continuation of the Helmholtz equation
- Acoustic and electromagnetic equations. Integral representations for harmonic problems