Examples of exponential instability for inverse inclusion and scattering problems
From MaRDI portal
Publication:4407151
DOI10.1088/0266-5611/19/3/313zbMath1033.35137arXivmath/0303126OpenAlexW2056663046MaRDI QIDQ4407151
Publication date: 26 June 2003
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0303126
Boundary value problems for second-order elliptic equations (35J25) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Numerical solution to inverse problems in abstract spaces (65J22)
Related Items
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond ⋮ A parabolic inverse problem with mixed boundary data. Stability estimates for the unknown boundary and impedance ⋮ The Calderón Problem for the Fractional Wave Equation: Uniqueness and Optimal Stability ⋮ Machine learning based data retrieval for inverse scattering problems with incomplete data ⋮ Unnamed Item ⋮ Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements ⋮ Stable determination of an inhomogeneous inclusion in a layered medium ⋮ On instability mechanisms for inverse problems ⋮ On the data completion problem and the inverse obstacle problem with partial Cauchy data for Laplace’s equation ⋮ High‐frequency stability estimates for a partial data inverse problem ⋮ Optimal identification of cavities in the generalized plane stress problem in linear elasticity ⋮ Stable Determination of an Inclusion in a Layered Medium with Special Anisotropy ⋮ Stable determination of an inclusion for a class of anisotropic conductivities ⋮ Refined instability estimates for some inverse problems ⋮ Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data ⋮ Optimal three spheres inequality at the boundary for the Kirchhoff-Love plate's equation with Dirichlet conditions ⋮ On inverse problems in secondary oil recovery ⋮ Increasing Stability in Acoustic and Elastic Inverse Source Problems ⋮ A New Method for the Data Completion Problem and Application to Obstacle Detection ⋮ Optimal Stability in the Identification of a Rigid Inclusion in an Isotropic Kirchhoff--Love Plate ⋮ Stability properties of an inverse parabolic problem with unknown boundaries ⋮ Exponential instability in the inverse scattering problem on the energy interval ⋮ On the Inverse Source Problem with Boundary Data at Many Wave Numbers ⋮ Exponential instability in the fractional Calderón problem ⋮ Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics ⋮ Computing volume bounds of inclusions by EIT measurements ⋮ Instability in the Gel'fand inverse problem at high energies ⋮ Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems ⋮ Quantitative estimates of strong unique continuation for wave equations ⋮ Stable determination of a body immersed in a fluid: the nonlinear stationary case ⋮ A remark on a paper by Alessandrini and Vessella ⋮ Exponential instability in the Gel'fand inverse problem on the energy intervals ⋮ Open issues of stability for the inverse conductivity problem ⋮ Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit ⋮ Evaluating the volume of a hidden inclusion in an elastic body ⋮ Stable determination of an inhomogeneous inclusion by local boundary measurements ⋮ Interior decay of solutions to elliptic equations with respect to frequencies at the boundary ⋮ Stable Determination of a Rigid Scatterer in Elastodynamics ⋮ CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS ⋮ Target Reconstruction with a Reference Point Scatterer using Phaseless Far Field Patterns ⋮ Stability and the inverse gravimetry problem with minimal data ⋮ Lipschitz stability for the inverse conductivity problem ⋮ On the inverse gravimetry problem with minimal data ⋮ Optimality of Increasing Stability for an Inverse Boundary Value Problem