Journal ArticleDOI
Stable determination of conductivity by boundary measurements
TLDR
In this paper, the problem of determining the scalar coefficient γ in the elliptic equation div(γ grad u) = 0 in ω when, for every Dirichlet datum u = ∅ on ∂ω, the Neumann datum γ(∂/ ∂ n)u = ∧.γ∅ is known.Abstract:
We consider the problem of determining the scalar coefficient γ in the elliptic equation div(γ grad u) = 0 in ω when, for every Dirichlet datum u = ∅ on ∂ω , the Neumann datum γ(∂/ ∂ n)u = ∧.γ∅ is known. We prove a continuous dependence resultread more
Citations
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Electrical Impedance Tomography
TL;DR: A survey of the work in electrical impedance tomography can be found in this article, where the authors survey some of the most important works in the field. Butt.t.
Journal ArticleDOI
Global uniqueness for a two-dimensional inverse boundary value problem
TL;DR: In this article, it was shown that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary.
Journal ArticleDOI
Reconstructions from boundary measurements
TL;DR: In this paper, the authors define la forme quadratique Qγ sur H 1/2 (∂Ω) par Qγ(f)=∫ Ω γ(x)|⊇u (x)| 2 dx ou u∈H 1 (Ω), est la solution unique a Lγu=0 dans Ω, u| ∂ Ω =f.
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Electrical impedance tomography
TL;DR: In this article, the authors review theoretical and numerical studies of the inverse problem of electrical impedance tomography, which seeks the electrical conductivity and permittivity inside a body, given simultaneous measurements of electrical currents and potentials at the boundary.
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Electrical impedance tomography and Calderón's problem
TL;DR: In this paper, the authors survey mathematical developments in the inverse method of electrical impedance tomography which consists in determining the electrical properties of a medium by making voltage and current measurements at the boundary of the medium.
References
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Journal ArticleDOI
A global uniqueness theorem for an inverse boundary value problem
John Sylvester,Gunther Uhlmann +1 more
TL;DR: In this paper, the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed region 2 C R', n? 3.
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Determining conductivity by boundary measurements
Robert V. Kohn,Michael Vogelius +1 more
TL;DR: In this article, Calderon poses the question: "Is it possible to determine the conductivite thermique of an object by means of mesures statiques de la temperature and du flux de chaleur a la limite?"
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Determining conductivity by boundary measurements II. Interior results
Robert V. Kohn,Michael Vogelius +1 more
TL;DR: In this article, it was shown that a three times continuously differentiable conductivity is identifiable by boundary measurements, and that a similar result holds for piecewise real-analytic conductivities.