Nachman's reconstruction method for the Calderón problem with discontinuous conductivities

George Lytle; Peter Perry; Samuli Siltanen

doi:10.1088/1361-6420/ab5a12

Nachman's reconstruction method for the Calderón problem with discontinuous conductivities

George Lytle, Peter Perry, Samuli Siltanen

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We show that Nachman's integral equations for the Calderón problem, derived for conductivities in W^2,p(ω), still hold for L^∝ conductivities which are 1 in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of L^∝ conductivities. We rely on Astala-Päivärinta's formulation of the Calderón problem for a framework in which these convergence results make sense.

Original language	English
Article number	035018
Journal	Inverse Problems
Volume	36
Issue number	3
DOIs	https://doi.org/10.1088/1361-6420/ab5a12
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd.

Keywords

Calderón problem
complex geometric optics solutions
conductivity equation
electrical impedance tomography
nonlinear Fourier transform

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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10.1088/1361-6420/ab5a12

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title = "Nachman's reconstruction method for the Calder{\'o}n problem with discontinuous conductivities",

abstract = "We show that Nachman's integral equations for the Calder{\'o}n problem, derived for conductivities in W2,p(ω), still hold for L∝ conductivities which are 1 in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of L∝ conductivities. We rely on Astala-P{\"a}iv{\"a}rinta's formulation of the Calder{\'o}n problem for a framework in which these convergence results make sense.",

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AU - Perry, Peter

AU - Siltanen, Samuli

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N2 - We show that Nachman's integral equations for the Calderón problem, derived for conductivities in W2,p(ω), still hold for L∝ conductivities which are 1 in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of L∝ conductivities. We rely on Astala-Päivärinta's formulation of the Calderón problem for a framework in which these convergence results make sense.

AB - We show that Nachman's integral equations for the Calderón problem, derived for conductivities in W2,p(ω), still hold for L∝ conductivities which are 1 in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of L∝ conductivities. We rely on Astala-Päivärinta's formulation of the Calderón problem for a framework in which these convergence results make sense.

KW - Calderón problem

KW - complex geometric optics solutions

KW - conductivity equation

KW - electrical impedance tomography

KW - nonlinear Fourier transform

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JO - Inverse Problems

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ER -

Nachman's reconstruction method for the Calderón problem with discontinuous conductivities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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