On an inverse boundary value problem

By Alberto P. Calderó. 2006

1,254 citations recorded by the source corpus.

This paper is a reprint of the original work by A. P. Calderon published by the Brazilian Mathematical Society (SBM) in ATAS of SBM (Rio de Janeiro), pp. 65-73, 1980. The original paper had no abstract, so this reprint to be truthful to the original work is published with no abstract.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68972043c5b31d8ae235228186a49af6cea2006c

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Calderóns' Inverse Problem for Anisotropic Conductivity in the Plane (2004, background): “In 1980 it was proposed by A. Calderon [ 9 ] that in the isotropic case any bounded conductivity (x) might be determined solely from the boundary measurements, i.e., from . Recently this has been confirmed in the two dimensional case (c.f.”
An inverse problem for a semi-linear elliptic equation in Riemannian geometries (2019, neutral): “In this case, the problem reduces to a version of the Calderón conjecture [2].”
Calderon inverse Problem with partial data on Riemann Surfaces (2009, background): “Introduction The problem of determining the potential in the Schrödinger operator by boundary measurement goes back to Calderón [8].”
The Calderón problem with partial data (2004, background): “Substantial progress has been made on this problem since Calder´ on’s pioneer contribution [ 3 ], and is also known as Calder´ on’s problem, in the case where the measurements are made on the whole boundary.”
Distributed shape derivative via averaged adjoint method and applications (2015, methodology): “5 Electrical impedance tomography We consider an application of the results above to a typical and important interface problem: the inverse problem of electrical impedance tomography (EIT) also known as the inverse conductivity or Calderón’s problem [6] in the mathematical literature.”
An analysis of electrical impedance tomography with applications to Tikhonov regularization (2012, background): “For instance, it was already noted in the pioneering work [9] that the forward map is analytic in σ with respect to the L∞-norm.”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “The inverse conductivity problem posed by Calderón [17] is the problem of determining whether a strictly positive γ ∈ L(D) is uniquely determined by Λγ and calculating γ in terms of Λγ if possible.”
The fractional Calderón problem: Low regularity and stability (2017, background): “The inverse conductivity problem posed by Calderón [Ca80] asks to determine the electrical conductivity of a medium from measurements of electrical voltage and current on its boundary.”
Inverse Problems for Nonsmooth First Order Perturbations of the Laplacian (2004, background): “Recently, the question was solved completely by Astala-Päivärinta [4], who showed using quasiconformal maps that the Dirichlet-to-Neumann map uniquely determines a L∞ conductivity, thus proving the original conjecture of Calderón in two dimensions.”
On uniqueness in the inverse conductivity problem with local data (2007, background): “Calderon [5] proposed the idea of using complex exponential solutions to demonstrate uniqueness in the linearized inverse condictivity problem.”
Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets (2012, background): “A paradigm problem of this type is Calderón’s inverse problem [13] that concerns the determination of the conductivity from the elliptic Dirichlet-to-Neumann map.”
The Calderón problem in transversally anisotropic geometries (2013, positive): “Starting from the pioneering works [7], [41], the standard approach for proving uniqueness results for the Calderón problem is based on special complex geometrical optics solutions to elliptic equations.”