On nonuniqueness for Calderón’s inverse problem

By Allan Greenleaf, Matti Lassas, Gunther Uhlmann. 2003

422 citations recorded by the source corpus.

We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.

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

View Paper: https://www.semanticscholar.org/paper/3fd24779abccb11a61aaa6bf26de7d7c8091fb3d

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In Computational Theory and Mathematics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Cloaking via change of variables for the Helmholtz equation (2010, methodology): “The arguments in [7, 21] applied to Helmholtz suggest that B1 should be cloaked by Ac = (F0)∗I ,qc = (F0)∗1, whereF0 = limρ→0 Fρ is the singular transformation that blows up the origin to the ball B1.”
Cloaking via change of variables in electric impedance tomography (2008, methodology): “Actually, (i) was settled for electric impedance tomography by [19] in space dimension n 3, using a method that does not work in space dimension two.”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “Counterexamples can be found when the conductivity is allowed to be only positive semi-definite [30, 31, 61].”
On modifications of Newton's second law and linear continuum elastodynamics (2007, background): “The recent recognition of possibilities for designing materials for ‘cloaking’ objects to electric fields and more generally to electromagnetic radiation (Greenleaf et al. 2003; Alú & Engheta 2005; Leonhardt 2006; Milton & Nicorovici 2006; Pendry et al. 2006) and for realizing phenomena such as ‘sup”