Electrical impedance tomography and Calderón's problem

By Gunther Uhlmann. 2009

433 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0a8d043a2eef851d43fd93cdf75423451dd74d6a

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In Biomedical Engineering

In Electrical and Electronic Engineering

In Mathematical Physics

Citations in the corpus

Inverse problems for elliptic equations with power type nonlinearities (2019, background): “There is an extensive theory concerning inverse boundary value problems for linear elliptic equations, and we refer to [Uhl09] for a survey.”
Determining an Unbounded Potential from Cauchy Data in Admissible Geometries (2011, background): “This problem has been extensively studied and we refer to [30] for a recent survey.”
The higher order fractional Calderón problem for linear local operators: Uniqueness (2020, background): “This is a nonlocal (fractional) counterpart of the classical Calderón problem arising in electrical impedance tomography where one obtains information about the electrical properties of some bounded domain by doing voltage and current measurements on the boundary [39, 40].”
Global uniqueness for the fractional semilinear Schrödinger equation (2017, methodology): “We refer to the survey paper [15] for recent developments in inverse boundary value problems for linear”
The Calderón problem in transversally anisotropic geometries (2013, background): “ssume in addition that the ray transform in the transversal manifold is injective. If Cg,q1 = Cg,q2, then q1 = q2. Starting from the pioneering works [9], [15], [19], [38], [40], [51], see also [41], [54], the standard approach for proving uniqueness and reconstruction results for the Calder´on prob”
The Calderón problem for variable coefficients nonlocal elliptic operators (2017, methodology): “We refer readers to a survey article [49] for more information.”