Calderon's inverse conductivity problem in the plane

By Kari ASTALA *, Lassi PÄIVÄRINTA #. 2006

652 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e43205be1f3fd5156d8cb40b1a4db8edc64a4d3a

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In Computational Theory and Mathematics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Differential operators for a scale of Poisson type kernels in the unit disc (2014, background): “Formula (1.5) points at a relation to so-called conductivity equations considered by Astala and Päivärinta [5] and others.”
Two-phase problems with distributed sources: regularity of the free boundary (2012, methodology): “The terminology comes from the connection of the Schrödinger inverse problem at zero energy with Calderón’s inverse conductivity problem [Calderón 1980] (see [Nachman 1996] for a solution for conductivities σ ∈W 2,p via the scattering transform, and see [Astala and Päivärinta 2006] for the solution ”
On uniqueness in the inverse conductivity problem with local data (2007, methodology): “Using these methods Nachman [17] demonstrated uniqueness of a ∈ C(2)(Ω̄) and Astala and Päivärinta [1] showed uniqueness of a ∈ L∞(Ω) which is a final result in the inverse conductivity problem in R(2) with many measurements from the whole boundary.”
The Calderón Problem with Partial Data for Less Smooth Conductivities (2006, neutral): “Recently Calderón’s problem in dimension two was settled in the affirmative for conductivities γ ∈ L∞(Ω) by Astala and Päivärinta [AP03] In recent years much attention has been devoted to the inverse problem, where only partial information about the Dirichlet to Neumann map is given.”
Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples (2012, methodology): “to solve inverse problems, see [Astala and Päivärinta, 2006; Nachman, 1988, 1996; Nachman, Sylvester and Uhlmann, 1988; Sylvester and Uhlmann, 1987], to detect spurious eigenvalues in numerical calculations, see [Brown and Marletta, 2004; Marletta, 2004, 2010] and to prove inequalities between Diric”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, methodology): “Reduction to one derivative was provided in [14], and Calderón’s original L question was answered in [1].”
Electrical impedance tomography and Calderón's problem (2009, methodology): “In the case of non-smooth coefficients, the function Mμ grows sub-exponentially in k. Astala and Päivärinta introduce the ‘transport matrix’ to deal with this problem.”
The Calderón inverse problem for isotropic quasilinear conductivities (2021, result): “This includes results in dimension two [3, 39], results with less regular conductivities [1, 17], results with measurements restricted to some portion of the boundary [4, 21, 25] and results in the setting of Riemannian manifolds [12, 16, 34, 28].”
An analysis of electrical impedance tomography with applications to Tikhonov regularization (2012, methodology): “Let r ∈ [1, 2) and the solution θ† fulfill Assumption 4.”
Limiting Carleman weights and anisotropic inverse problems (2008, methodology): “The regularity was improved by Sun and Uhlmann [30] to Lipschitz conductivities using the techniques of Brown and Uhlmann [5], and to L∞ conductivities by Astala-Lassas-Päivärinta [2] using the work of Astala-Päivärinta [3].”
GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES (2014, background): “The two–dimensional problem has different mathematical properties (see [3] for the solution of the uniqueness problem).”
Monotonicity and local uniqueness for the Helmholtz equation (2017, background): “For a short list of seminal contributions for full boundary data let us refer to [Kohn and Vogelius 1984; 1985; Druskin 1998; Sylvester and Uhlmann 1987; Nachman 1996; Astala and Päivärinta 2006; Haberman and Tataru 2013; Caro and Rogers 2016].”
Calderon inverse Problem with partial data on Riemann Surfaces (2009, neutral): “Recently a new approach developed by Astala and Päivärinta in [2] improved this result to assuming that the conductivity is only a L∞ scalar function.”