Lipschitz stability for the inverse conductivity problem

DOI10.1016/j.aam.2004.12.002zbMath1095.35058OpenAlexW2095463076MaRDI QIDQ2573656

Sergio Vessella, Giovanni Alessandrini

Publication date: 22 November 2005

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2004.12.002

zbMATH Keywords

Dirichlet-to-Neumann map continuous dependence unknown conductivity

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30)

Related Items (89)

Lipschitz Stable Determination of Polyhedral Conductivity Inclusions from Local Boundary Measurements ⋮ A novel two-point gradient method for regularization of inverse problems in Banach spaces ⋮ On Uniqueness of Recovering Coefficients from Localized Dirichlet-to-Neumann Map for Piecewise Homogeneous Piezoelectricity ⋮ Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation ⋮ A Lipschitz stable reconstruction formula for the inverse problem for the wave equation ⋮ Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming ⋮ A remark on Lipschitz stability for inverse problems ⋮ Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability ⋮ A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities ⋮ EIT and the average conductivity ⋮ Inverse problems on low-dimensional manifolds ⋮ On the tangential cone condition for electrical impedance tomography ⋮ Novel multi-level projected iteration to solve inverse problems with nearly optimal accuracy ⋮ Quadratic convergence of Levenberg-Marquardt method for elliptic and parabolic inverse robin problems ⋮ A Mumford-Shah-type approach to simultaneous reconstruction and segmentation for emission tomography problems with Poisson statistics ⋮ Uniqueness in the Inverse Boundary Value Problem for Piecewise Homogeneous Anisotropic Elasticity ⋮ Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE ⋮ On variational regularization: finite dimension and Hölder stability ⋮ Iteratively regularized Landweber iteration method: convergence analysis via Hölder stability ⋮ Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements ⋮ Calderón's inverse problem with a finite number of measurements II: independent data ⋮ On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem ⋮ Lipschitz stability at the boundary for time-harmonic diffuse optical tomography ⋮ Multiple level sets for piecewise constant surface reconstruction in highly ill-posed problems ⋮ Reconstruction of the derivative of the conductivity at the boundary ⋮ On instability mechanisms for inverse problems ⋮ On (global) unique continuation properties of the fractional discrete Laplacian ⋮ Stability Estimates for the Inverse Fractional Conductivity Problem ⋮ Fréchet differentiability of the elasto-acoustic scattered field with respect to Lipschitz domains ⋮ Convergence analysis of an optimally accurate frozen multi-level projected steepest descent iteration for solving inverse problems ⋮ A high order discontinuous Galerkin method for the recovery of the conductivity in electrical impedance tomography ⋮ Determining an anisotropic conductivity by boundary measurements: stability at the boundary ⋮ Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case ⋮ Conformal mapping for cavity inverse problem: an explicit reconstruction formula ⋮ Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT ⋮ Characterization for stability in planar conductivities ⋮ Time-harmonic diffuse optical tomography: Hölder stability of the derivatives of the optical properties of a medium at the boundary ⋮ Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data ⋮ Determination of piecewise homogeneous sources for elastic and electromagnetic waves ⋮ Improved local convergence analysis of the Landweber iteration in Banach spaces ⋮ Calderón's problem for some classes of conductivities in circularly symmetric domains ⋮ Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves ⋮ Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes ⋮ Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem ⋮ Uniqueness and Lipschitz stability for the identification of Lamé parameters from boundary measurements ⋮ Convergence rates for iteratively regularized Gauss-Newton method subject to stability constraints ⋮ An introduction to finite element methods for inverse coefficient problems in elliptic PDEs ⋮ Lipschitz stability for an inverse source scattering problem at a fixed frequency ^* ⋮ Stability estimates for recovering the potential by the impedance boundary map ⋮ Computing volume bounds of inclusions by EIT measurements ⋮ Stability of Calderón inverse conductivity problem in the plane ⋮ Instability in the Gel'fand inverse problem at high energies ⋮ Locality estimates for Fresnel-wave-propagation and stability of x-ray phase contrast imaging with finite detectors ⋮ Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem ⋮ Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface ⋮ Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities ⋮ Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem ⋮ Inverse problems: seeing the unseen ⋮ A remark on a paper by Alessandrini and Vessella ⋮ Reconstruction of a Piecewise Smooth Absorption Coefficient by an Acousto-Optic Process ⋮ Open issues of stability for the inverse conductivity problem ⋮ Electrical Impedance Tomography ⋮ Iterative reconstruction of the wave speed for the wave equation with bounded frequency boundary data ⋮ Stable determination of an inhomogeneous inclusion by local boundary measurements ⋮ An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints ⋮ Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain ⋮ Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability ⋮ CGO-Faddeev approach for complex conductivities with regular jumps in two dimensions ⋮ A transmission problem on a polygonal partition: regularity and shape differentiability ⋮ The Local Calderòn Problem and the Determination at the Boundary of the Conductivity ⋮ Inverse problem for the Helmholtz equation with Cauchy data: reconstruction with conditional well-posedness driven iterative regularization ⋮ Infinite-dimensional inverse problems with finite measurements ⋮ Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates ⋮ CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS ⋮ A priori estimates of attraction basins for nonlinear least squares, with application to Helmholtz seismic inverse problem ⋮ Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case ⋮ Stability and reconstruction for inverse corrosion problems ⋮ New global stability estimates for the Calderón problem in two dimensions ⋮ On statistical Calderón problems ⋮ Stability estimates for an inverse problem for the Schrödinger equation at negative energy in two dimensions ⋮ Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime ⋮ Lipschitz Stable Determination of Polygonal Conductivity Inclusions in a Two-Dimensional Layered Medium from the Dirichlet-to-Neumann Map ⋮ Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional ⋮ On the uniqueness of inverse problems for the reduced wave equation with unknown embedded obstacles ⋮ Convergence analysis of iteratively regularized Gauss-Newton method with frozen derivative in Banach spaces ⋮ Bridging and Improving Theoretical and Computational Electrical Impedance Tomography via Data Completion ⋮ Stability of the Calderón problem in admissible geometries ⋮ Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners ⋮ 30 years of Calderón's problem

Cites Work

This page was built for publication: Lipschitz stability for the inverse conductivity problem