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Inverse problems: seeing the unseen (Q5172853)

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scientific article; zbMATH DE number 6398509

Language	Label	Description	Also known as
English	Inverse problems: seeing the unseen	scientific article; zbMATH DE number 6398509

Statements

scholarly article

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Inverse problems: seeing the unseen (English)

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zbMATH Open document ID

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10.1007/s13373-014-0051-9

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Gunther Uhlmann

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Bulletin of Mathematical Sciences

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publication date

5 February 2015

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Mathematics Subject Classification ID

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zbMATH DE Number

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s13373-014-0051-9

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On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation

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Inverse boundary problems for systems in two dimensions

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Stable determination of conductivity by boundary measurements

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Singular solutions of elliptic equations and the determination of conductivity by boundary measurements

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Open issues of stability for the inverse conductivity problem

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Lipschitz stability for the inverse conductivity problem

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Structure of the Semi-Classical Amplitude for General Scattering Relations

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Reconstruction of the potential from partial Cauchy data for the Schroedinger equation

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Calderón's inverse conductivity problem in the plane

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Calderóns' Inverse Problem for Anisotropic Conductivity in the Plane

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Inverse transport with isotropic sources and angularly averaged measurements

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Quantitative thermo-acoustics and related problems

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Inverse diffusion theory of photoacoustics

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Reconstructions for some coupled-physics inverse problems

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Reconstruction of Coefficients in Scalar Second-Order Elliptic Equations from Knowledge of Their Solutions

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Stability of Calderón inverse conductivity problem in the plane

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The Calderon Problem for Two-Dimensional Manifolds by the BC-Method

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To the reconstruction of a riemannian manifold via its spectral data (Bc–Method)

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Entropy and rigidity of locally symmetric spaces of strictly negative curvature

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Stability and uniqueness of the solution of the inverse kinematic problem of seismology in higher dimensions

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Well-posedness of the Goursat problem and stability for point source inverse backscattering

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Electrical impedance tomography

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Resistor network approaches to electrical impedance tomography

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Recovering the conductivity at the boundary from the Dirichlet to Neumann map: a pointwise result

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On a quasilinear inverse boundary value problem

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Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions

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Recovering a potential from Cauchy data in the two-dimensional case

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RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA

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Boundary rigidity and filling volume minimality of metrics close to a flat one

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Semiclassical Pseudodifferential Calculus and the Reconstruction of a Magnetic Field

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Remark on extensions of the Watermelon theorem

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Exponentially Growing Solutions for Nonsmooth First-Order Perturbations of the Laplacian

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Inverse Boundary Value Problem for Maxwell Equations with Local Data

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A Problem in Electrical Prospection and a n-Dimensional Borg-Levinson Theorem

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Quantitative photo-acoustic tomography with partial data

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Electrical Impedance Tomography

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Rigidity and the distance between boundary points

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Rigidity for surfaces of non-positive curvature

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Local boundary rigidity of a compact Riemannian manifold with curvature bounded above

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Conjugacy and rigidity for manifolds with a parallel vector field

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On the linearized local Calderón problem

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Reconstructing the metric and magnetic field from the scattering relation

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Determining a magnetic Schrödinger operator from partial Cauchy data

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Limiting Carleman weights and anisotropic inverse problems

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Fourier integral operators. II

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On the inverse boundary value problem for linear isotropic elasticity

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A periodic Faddeev-type solution operator

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Recovering a complex coefficient in a planar domain from the Dirichlet-to-Neumann map

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Elliptic partial differential equations of second order

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Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics

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Invisibility and inverse problems

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The Calderón problem for conormal potentials I: Global uniqueness and reconstruction

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On nonuniqueness for Calderón's inverse problem

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Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform

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Filling Riemannian manifolds

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Inverse problems for Einstein manifolds

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Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

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Calderón inverse problem with partial data on Riemann surfaces

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Identification of a connection from Cauchy data on a Riemann surface with boundary

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Sojourn times and asymptotic properties of the scattering matrix

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Recent progress in electrical impedance tomography

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Uniqueness in Calderón's problem with Lipschitz conductivities

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Stability estimates for the inverse boundary value problem by partial Cauchy data

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Inverse conductivity problem on Riemann surfaces

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Probing for electrical inclusions with complex spherical waves

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How to draw a picture of an unknown inclusion from boundary measurements. Two mathematical inversion algorithms

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Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements

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Inverse Boundary Value Problem for Schrödinger Equation in Two Dimensions

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The Calderón problem with partial data in two dimensions

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Determination of second-order elliptic operators in two dimensions from partial Cauchy data

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Partial Cauchy data for general second order elliptic operators in two dimensions

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Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets

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On uniqueness of Lamé coefficients from partial Cauchy data in three dimensions

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Comment on Calderon's Paper: "On an Inverse Boundary Value Problem"

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On uniqueness in the inverse conductivity problem with local data

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On uniqueness in inverse problems for semilinear parabolic equations

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Completeness of products of solutions and some inverse problems for PDE

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Global Uniqueness for a Two-Dimensional Semilinear Elliptic Inverse Problem

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Global uniqueness for a semilinear elliptic inverse problem

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Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in Euclidean space

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Hyperbolic geometry and local Dirichlet-Neumann map

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Inverse problems for the Pauli Hamiltonian in two dimensions

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Inverse problems for the anisotropic Maxwell equations

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The Calderón problem with partial data

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The Calderón Problem with Partial Data for Less Smooth Conductivities

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Determining nonsmooth first order terms from partial boundary measurements

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Acousto-electric tomography and CGO solutions with internal data

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The Inverse Conductivity Problem with an Imperfectly Known Boundary

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Cloaking via change of variables in electric impedance tomography

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Determining conductivity by boundary measurements

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Determining conductivity by boundary measurements II. Interior results

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Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary

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Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain

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Determining a first order perturbation of the biharmonic operator by partial boundary measurements

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Inverse boundary value problems for the perturbed polyharmonic operator

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Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential

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Determining anisotropic real-analytic conductivities by boundary measurements

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Inverse problems with partial data in a slab

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Semiglobal boundary rigidity for Riemannian metrics

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On determining a Riemannian manifold from the Dirichlet-to-Neumann map

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The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary

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Optical Conformal Mapping

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Exponential instability in an inverse problem for the Schrödinger equation

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Sur la rigidite imposee par la longueur des geodesiques

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Restriction de la distance géodésique à un arc et rigidité

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A problem of reconstructing a Riemannian metric

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Global uniqueness for a two-dimensional inverse boundary value problem

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Reconstructions from boundary measurements

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A Multidimensional Inverse-Scattering Method

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Reconstruction in the Calderón Problem with Partial Data

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A depth-dependent stability estimate in electrical impedance tomography

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Reconstruction of Penetrable Obstacles in Acoustic Scattering

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Local determination of conductivity at the boundary from the Dirichlet-to-Neumann map

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Global uniqueness for an inverse boundary problem arising in elasticity

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Inverse Problems at the Boundary for an Elastic Medium

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Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field

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Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)

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The $ \bar\partial$-equation in the multidimensional inverse scattering problem

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An inverse boundary value problem in electrodynamics

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Electromagnetic Inverse Problems and Generalized Sommerfeld Potentials

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On the length of the geodesics of a metric of negative curvature on the disc.

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The attenuated ray transform for connections and Higgs fields

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Tensor tomography on surfaces

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Complex geometrical optics solutions for Lipschitz conductivities.

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Controlling Electromagnetic Fields

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Integral geometry of tensor fields on a manifold of negative curvature

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The boundary distance function and the Dirichlet-to-Neumann map

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Recovery of the potential from fixed-energy scattering data

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Inverse problems with partial data for a Dirac system: a Carleman estimate approach

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Complex spherical waves and inverse problems in unbounded domains

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A Backprojection Algorithm for Electrical Impedance Imaging

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Variations of Dirichlet-to-Neumann map and deformation boundary rigidity of simple 2-manifolds

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On deformation boundary rigidity and spectral rigidity of Riemannian surfaces with no focal points.

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Stability for the reconstruction of a Riemannian metric by boundary measurements

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A linearized inverse boundary value problem for Maxwell's equations

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Recent progress on the boundary rigidity problem

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Rigidity for metrics with the same lengths of geodesics

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Stability estimates for the \(X\)-ray transform of tensor fields and boundary rigidity

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Boundary rigidity and stability for generic simple metrics

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Integral geometry of tensor fields on a class of non-simple Riemannian manifolds

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Local Lens rigidity with incomplete data for a class of non-simple Riemannian manifolds

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Anisotropic inverse problems in two dimensions

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Generic uniqueness for an inverse boundary value problem

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Inverse problems in quasilinear anisotropic media

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An anisotropic inverse boundary value problem

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A global uniqueness theorem for an inverse boundary value problem

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A uniqueness theorem for an inverse boundary value problem in electrical prospection

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Unique continuation for solutions to pde's; between hörmander's theorem and holmgren' theorem

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The Schrodinger operator in the plane

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Inverse boundary value problems for partial differential equations

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Low-energy inverse problems in three-body scattering

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Complex Spherical Waves for the Elasticity System and Probing of Inclusions

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Reconstructing Discontinuities Using Complex Geometrical Optics Solutions

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Reconstructing electromagnetic obstacles by the enclosure method

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