# Reconstruction of a potential from the impedance boundary map

@article{Isaev2012ReconstructionOA, title={Reconstruction of a potential from the impedance boundary map}, author={Mikhail Isaev and Roman G. Novikov}, journal={arXiv: Analysis of PDEs}, year={2012} }

We give formulas and equations for finding generalized scattering data for the Schr\"odinger equation in open bounded domain at fixed energy from the impedance boundary map (or Robin-to-Robin map). Combining these results with results of the inverse scattering theory we obtain efficient methods for reconstructing potential from the impedance boundary map.

## 13 Citations

Stability estimates for recovering the potential by the impedance boundary map

- Mathematics
- 2013

The impedance boundary map (or Robin-to-Robin map) is studied for the Schrödinger equation in an open bounded domain for fixed energy in the multidimensional case. Global stability estimates are…

Finding scattering data for a time-harmonic wave equation with first order perturbation from the Dirichlet-to-Neumann map

- Mathematics
- 2015

Abstract We present formulas and equations for finding scattering data from the Dirichlet-to-Neumann map for a time-harmonic wave equation with first order perturbation with compactly supported…

On the reconstruction of parameters of a moving fluid from the Dirichlet-to-Neumann map

- Mathematics
- 2015

We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the…

The inverse Robin boundary value problem in a half-space

- Mathematics
- 2013

We study the inverse Robin problem for the Schrödinger equation in a half-space. The potential differing from a constant is assumed to be compactly supported. We first solve the direct problem for…

Direct inversion from partial-boundary data in electrical impedance tomography

- Mathematics
- 2016

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the…

Instability in the Gel'fand inverse problem at high energies

- Physics, Mathematics
- 2012

We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on…

Instability in the Gel'fand inverse problem at high energies

- Mathematics
- 2013

We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceding stability results on…

Creation and annihilation of point-potentials using Moutard-type transform in spectral variable

- Physics, Mathematics
- 2019

We continue to develop the method for creation and annihilation of contour singularities in the $\bar\partial$--spectral data for the two-dimensional Schr\"odinger equation at fixed energy. Our…

CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS

- MathematicsForum of Mathematics, Sigma
- 2019

We prove that an $L^{\infty }$ potential in the Schrödinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a…

Energy and regularity dependent stability estimates for the Gel'fand inverse problem in multidimensions

- Mathematics
- 2012

We prove new global Holder-logarithmic stability estimates for the Gel'fand inverse problem at fixed energy in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference…

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