On nonuniqueness for Calderón's inverse problem
From MaRDI portal
Publication:1429373
DOI10.4310/MRL.2003.v10.n5.a11zbMath1054.35127arXivmath/0302258MaRDI QIDQ1429373
Gunther Uhlmann, Allan Greenleaf, Matti Lassas
Publication date: 18 May 2004
Published in: Mathematical Research Letters (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0302258
Dirichlet-to-Neumann mapnonuniquenessisotropic conductivityanisotropic conductivitiesCalderón's inverse problem
Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30)
Related Items
Far field broadband approximate cloaking for the Helmholtz equation with a Drude-Lorentz refractive index ⋮ Cloaking magnetic field and generating electric field with topological insulator and high permeability material ⋮ A Mathematical Theory of Microscale Hydrodynamic Cloaking and Shielding by Electro-Osmosis ⋮ Nearly non-scattering electromagnetic wave set and its application ⋮ Uniqueness and nonuniqueness in inverse problems for elliptic partial differential equations and related medical imaging ⋮ Inverse problems in imaging and engineering science ⋮ On waves in multi-scale chiral elastic systems ⋮ Determination of the spacetime from local time measurements ⋮ Approximate cloaking for the full wave equation via change of variables: the Drude-Lorentz model ⋮ Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds ⋮ On optimal cloaking-by-mapping transformations ⋮ Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations ⋮ Analysis of an approximate cloaking for acoustic scattering problems in \(\mathbb R^3\) ⋮ Existence of weakly neutral coated inclusions of general shape in two dimensions ⋮ Approximate isotropic cloak for the Maxwell equations ⋮ Nonscattering acoustic objects in a medium with a spherical stratification ⋮ Well-posedness study for a time-domain spherical cloaking model ⋮ Transformation method and wave control ⋮ Invisibility Cloaking and Transformation Optics for Three Dimensional Manifolds and Applications in Cosmology ⋮ On isotropic cloaking and interior transmission eigenvalue problems ⋮ Cloaking for a quasi-linear elliptic partial differential equation ⋮ Two-dimensional elastic scattering coefficients and enhancement of nearly elastic cloaking ⋮ A foliated and reversible Finsler manifold is determined by its broken scattering relation ⋮ On the inverse problem of finding cosmic strings and other topological defects ⋮ The Poisson embedding approach to the Calderón problem ⋮ Nonlinear pre-stress for cloaking from antiplane elastic waves ⋮ Nearly cloaking the elastic wave fields ⋮ Transformational cloaking from seismic surface waves by micropolar metamaterials with finite couple stiffness ⋮ Enhancement of near-cloaking. II: The Helmholtz equation ⋮ Enhancement of near cloaking using generalized polarization tensors vanishing structures. I: The conductivity problem ⋮ The light ray transform on Lorentzian manifolds ⋮ The anisotropic Calderón problem for singular metrics of warped product type: the borderline between uniqueness and invisibility ⋮ Bounds on Herglotz functions and fundamental limits of broadband passive quasistatic cloaking ⋮ On uniqueness and nonuniqueness for internal potential reconstruction in quantum fields from one measurement. II: The non-radial case ⋮ On uniqueness and nonuniqueness for internal potential reconstruction in quantum fields from one measurement ⋮ On the distribution of Born transmission eigenvalues in the complex plane ⋮ Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain ⋮ Near optimal pentamodes as a tool for guiding stress while minimizing compliance in \(3d\)-printed materials: a complete solution to the weak \(G\)-closure problem for \(3d\)-printed materials ⋮ On Electromagnetic Scattering from a Penetrable Corner ⋮ Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry ⋮ On Absence and Existence of the Anomalous Localized Resonance without the Quasi-static Approximation ⋮ Invisibility cloaking via non-smooth transformation optics and ray tracing ⋮ Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking due to anomalous localized resonance ⋮ Stability of stationary inverse transport equation in diffusion scaling ⋮ Counterexamples to uniqueness in the inverse fractional conductivity problem with partial data ⋮ Plasmonic cloaking and scattering cancelation for electromagnetic and acoustic waves ⋮ Numerical analysis of three-dimensional acoustic cloaks and carpets ⋮ Elastic cloaking theory ⋮ Non-uniqueness of time-domain reflection from 3D planar elastic layers ⋮ Acoustic cloaking transformations from attainable material properties ⋮ Nearly cloaking the full Maxwell equations: cloaking active contents with general conducting layers ⋮ Full-wave invisibility of active devices at all frequencies ⋮ Approximate acoustic cloaking in inhomogeneous isotropic space ⋮ Transformation optics with artificial Riemann sheets ⋮ Stress-wave energy management through material anisotropy ⋮ Determining a first order perturbation of the biharmonic operator by partial boundary measurements ⋮ Active manipulation of fields modeled by the Helmholtz equation ⋮ Uniqueness in Calderón's problem for conductivities with unbounded gradient ⋮ Total Reflection and Cloaking by Triangular Defects Embedded in Zero Index Metamaterials ⋮ On corners scattering stably and stable shape determination by a single far-field pattern ⋮ Acoustic cloaking theory ⋮ Approximate cloaking using transformation optics for acoustic and electromagnetic waves ⋮ Full and partial cloaking in electromagnetic scattering ⋮ Antiplane elastic wave cloaking using metamaterials, homogenization and hyperelasticity ⋮ Cloaking via change of variables for the Helmholtz equation ⋮ Inverse problems: seeing the unseen ⋮ Inverse problems and invisibility cloaking for FEM models and resistor networks ⋮ Acoustic band gaps in arrays of neutral inclusions ⋮ Focusing: coming to the point in metamaterials ⋮ Cloaking via change of variables for the Helmholtz equation in the whole space ⋮ Full range scattering estimates and their application to cloaking ⋮ On modifications of Newton's second law and linear continuum elastodynamics ⋮ Transformation cloaking in elastic plates ⋮ The Blow-up of Electromagnetic Fields in 3-Dimensional Invisibility Cloaking for Maxwell's Equations ⋮ Three-dimensional elastic scattering coefficients and enhancement of the elastic near cloaking ⋮ Stability of Inverse Transport Equation in Diffusion Scaling and Fokker--Planck Limit ⋮ Positive-energy D-bar method for acoustic tomography: a computational study ⋮ Cloaking via Mapping for the Heat Equation ⋮ Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticity ⋮ Cloaking using complementary media for the Helmholtz equation and a three spheres inequality for second order elliptic equations ⋮ Electromagnetic wormholes via handlebody constructions ⋮ ON NONUNIQUENESS FOR THE ANISOTROPIC CALDERÓN PROBLEM WITH PARTIAL DATA ⋮ Approximate cloaking for electromagnetic waves via transformation optics: Cloaking versus infinite energy ⋮ Approximate cloaking for the heat equation via transformation optics ⋮ Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary ⋮ Nonlinear and linear elastodynamic transformation cloaking ⋮ Coated inclusions of finite conductivity neutral to multiple fields in two-dimensional conductivity or anti-plane elasticity ⋮ Approximate Cloaking for Time-dependent Maxwell Equations via Transformation Optics ⋮ On Near-cloaking for Linear Elasticity ⋮ Counterexamples to inverse problems for the wave equation ⋮ Well-posedness study and finite element simulation of time-domain cylindrical and elliptical cloaks ⋮ Approximate cloaking for the Helmholtz equation via transformation optics and consequences for perfect cloaking ⋮ Perfect cloaking of ellipsoidal regions ⋮ The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds ⋮ A degenerate polar lattice for cloaking in full two-dimensional elastodynamics and statics ⋮ Cloaking of a circular cylindrical elastic inclusion from antiplane elastic waves and resonance effects ⋮ A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity ⋮ Invisibility and inverse problems ⋮ Regularized transformation-optics cloaking for the Helmholtz equation: from partial cloak to full cloak ⋮ Inverse boundary value problems for the perturbed polyharmonic operator ⋮ Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional ⋮ 30 years of Calderón's problem
