Stable determination of polygonal inclusions in Calderón’s problem by a single partial boundary measurement

DOI10.1088/1361-6420/ab9d6bzbMath1445.35334arXiv1902.04462OpenAlexW3036079693MaRDI QIDQ5117400

No author found.

Publication date: 25 August 2020

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.04462

zbMATH Keywords

electrical impedance tomographylogarithmic stabilitypiecewise conductivitiessingle partial boundary measurement

Mathematics Subject Classification ID

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

Related Items

Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunctions, On local and global structures of transmission eigenfunctions and beyond, Lipschitz Stable Determination of Polyhedral Conductivity Inclusions from Local Boundary Measurements, Inverse problems on low-dimensional manifolds, Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems, Shape reconstructions by using plasmon resonances, Stable determination of an elastic medium scatterer by a single far-field measurement and beyond, Boundary localization of transmission eigenfunctions in spherically stratified media, Two single-measurement uniqueness results for inverse scattering problems within polyhedral geometries, Lipschitz stability for an inverse source scattering problem at a fixed frequency ^*, Free boundary methods and non-scattering phenomena, On a local geometric property of the generalized elastic transmission eigenfunctions and application, On vanishing near corners of conductive transmission eigenfunctions, Lipschitz Stable Determination of Polygonal Conductivity Inclusions in a Two-Dimensional Layered Medium from the Dirichlet-to-Neumann Map, On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement, Boundary Homogenization of a Class of Obstacle Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A global uniqueness theorem for an inverse boundary value problem
• Corners always scatter
• An introduction to mathematics of emerging biomedical imaging
• An identification problem for an elliptic equation in two variables
• Reconstructions from boundary measurements
• On the electro-sensing of weakly electric fish
• Reconstruction of small inhomogeneities from boundary measurements
• Inverse inclusion problem: a stable method to determine disks
• On an inverse boundary value problem
• Calderón's inverse conductivity problem in the plane
• The Calderón problem with partial data
• Reconstruction of the support function for inclusion from boundary measurements
• Shape recognition and classification in electro-sensing
• Identification of an inclusion in multifrequency electric impedance tomography
• Oblique derivative and interface problems on polygonal domains and networks
• Polygonal interface problems:higher regularity results
• GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES
• The Calderón problem with partial data in two dimensions
• The stability for the Cauchy problem for elliptic equations
• Inverse Conductivity Problem with One Measurement: Error Estimates and Approximate Identification for Perturbed Disks
• Inverse Conductivity Problem with One Measurement: Uniqueness of Balls in $\Bbb R^3$
• Elliptic Equations in Divergence Form, Geometric Critical Points of Solutions, and Stekloff Eigenfunctions
• The Inverse Conductivity Problem with One Measurement: Uniqueness for Convex Polyhedra
• Corner Effects on the Perturbation of an Electric Potential
• Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities
• Stable determination of conductivity by boundary measurements
• Reconstruction of the potential from partial Cauchy data for the Schroedinger equation
• Logarithmic Convexity for Supremum Norms of Harmonic Functions
• The layer potential technique for the inverse conductivity problem
• Reconstruction of piecewise constant layered conductivities in electrical impedance tomography
• Numerical determination of anomalies in multifrequency electrical impedance tomography
• Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
• Factorization method and irregular inclusions in electrical impedance tomography