Related papers: Inverse conductivity problem in dimension two
In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…
The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…
We consider the elliptic estimates for Dirichlet-Neumann operator related to the water-wave problem on a two-dimensional corner domain in this paper. Due to the singularity of the boundary, there will be singular parts in the solution of…
We consider the Schrodinger operator in n-dimensional rectangular domains with either Dirichlet or Neumann boundary conditions on the faces and study the constraints on the potential imposed by fixing the spectrum of the operator.We study…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
In this paper, we study a new type of inverse problem on warped product Riemannian manifolds with connected boundary that we name warped balls. Using the symmetry of the geometry, we first define the set of Regge poles as the poles of the…
We consider the dynamical system with boundary control for the vector Schr\"odinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the…
We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…
The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of…
We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater…
A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The…
We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…
We present a procedure for recovering the conformal factor of an anisotropic conductivity matrix in a known conformal class in a domain in Euclidean space of dimension greater than or equal to 2. The method requires one internal…
We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to…
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated…
The original Calder\'on problem consists in recovering the potential (or the conductivity) from the knowledge of the related Neumann to Dirichlet map (or Dirichlet to Neumann map). Here, we first perturb the medium by injecting small-scaled…
We consider boundary measurements for the wave equation on a bounded domain $M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an…
In this paper, we consider the inverse eigenvalue problem for the positive doubly stochastic matrices, which aims to construct a positive doubly stochastic matrix from the prescribed realizable spectral data. By using the real Schur…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…