Journal ArticleDOI
Recovering a potential from Cauchy data in the two-dimensional case
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In this article, it was shown that the Cauchy data for the Schrödinger equation in the two-dimensional case determines a potential from Lp (for p > 2) uniquely.Abstract:
In this paper we prove that the Cauchy data for the Schrödinger equation in the two-dimensional case determines a potential from Lp (for p > 2) uniquely. We also obtain a linear inversion formula for smooth potentials.read more
Citations
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Journal ArticleDOI
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.
Journal ArticleDOI
Limiting Carleman weights and anisotropic inverse problems
TL;DR: In this article, the authors considered the anisotropic Calderon problem and related inverse problems, and characterized those Riemannian manifolds which admit limiting Carleman weights, and gave a complex geometrical optics construction for a class of such manifolds.
Journal ArticleDOI
Regularized d-bar method for the inverse conductivity problem
TL;DR: In this article, a strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143] for the ill-posed inverse conductivity problem is presented.
Journal ArticleDOI
The Calderón problem with partial data in two dimensions
TL;DR: In this paper, it was shown that the Cauchy data for the Schrodinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential, which is the case for the conductivity equation.
Journal ArticleDOI
Invisibility and inverse problems
TL;DR: This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.
References
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Book ChapterDOI
Elliptic Partial Differential Equations of Second Order
Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
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.
Journal ArticleDOI
On an inverse boundary value problem
TL;DR: A. P. Calderon as discussed by the authors published by the Brazilian Mathematical Society (SBM) in ATAS of SBM (Rio de Janeiro), pp. 65-73, 1980.
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
Calderon's inverse conductivity problem in the plane
Kari Astala,Lassi Päivärinta +1 more
TL;DR: In this paper, it was shown that the Dirichlet to Neumann map for the equation ∇·σ∇u = 0 in a two-dimensional domain uniquely determines the bounded measurable constant.
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