Calderóns' Inverse Problem for Anisotropic Conductivity in the Plane

By Kari ASTALA *, Lassi PÄIVÄRINTA #, Matti Lassas. 2004

185 citations recorded by the source corpus.

Abstract We study the inverse conductivity problem for an anisotropic conductivity σ ∈ L ∞ in bounded and unbounded domains. Also, we give applications of the results in the case when two sets of local boundary data are given.

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

View Paper: https://www.semanticscholar.org/paper/bfd05142174f018aafaaf80381b21db33bea2bb2

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In Computational Theory and Mathematics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Partial Cauchy data for general second order elliptic operators in two dimensions (2010, background): “, Γ̃ = ∂Ω) the question whether one can determine the conductivity up to the above limitation, has been solved in two dimensions for C(2) conductivities in [21], Lipschitz conductivities in [27] and merely L∞ conductivities in [2], [3].”
Stability of Calderón inverse conductivity problem in the plane (2007, background): “This approach have proved to be effective also when dealing with the anisotropic case, see [9].”
Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets (2012, background): “corresponding to a general Riemannian metric) in ˆRn, Calderon’s inverse problem was solved in two dimensions in [43] using the isotropic result [38]. The needed regularity was reduced to L1later in [4]. In the case of dimension n3, Calderon’s inverse problem is of geometrical nature and makes sense”
Calderon inverse Problem with partial data on Riemann Surfaces (2009, background): “d Pa¨iv¨arinta in [2] improved this result to assuming that the conductivity is only a L∞ scalar function. This was later generalized to L∞ anisotropic conductivities by Astala-Lassas-Pa¨iv¨arinta in [3]. We notice that there still are rather few results in the direction of recovering the Riemannian”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “For the case of anisotropic conductivities, see [2, 71, 85, 86].”
Limiting Carleman weights and anisotropic inverse problems (2008, methodology): “the techniques of Brown and Uhlmann [5], and to L∞ conductivities by Astala-Lassas-Päivärinta [2] using the work of Astala-Päivärinta [3].”
Inverse problems: seeing the unseen (2014, unknown): “In two dimensions this has been shown for L∞( ) conductivities in [12].”
Cloaking via change of variables in electric impedance tomography (2008, background): “The recent improvement in [5] assumes only that σ is bounded and positive-definite.”