Uniqueness in the Inverse Conductivity Problem for Conductivities with 3/2 Derivatives in Lp, p > 2n

By Russell M. Brown, Rodolfo H. Torres. 2003

123 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c777875e0bec275590cad25daaa2a55391387235

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “This result has been extended to conductivities having 32 derivatives in [13, 75], and in [29] for conductivities having C-smooth conormal singularities on submanifolds.”
Inverse problems: seeing the unseen (2014, background): “5 has been extended to conductivities having 3/2 derivatives in some sense in [32,152].”
Stability of Calderón inverse conductivity problem in the plane (2007, background): “In higher dimension the known results require some extra a priori regularity on γ, basically some control on 32 derivatives of γ, see [33], [13], [29] and [ 16 ].”
Electrical impedance tomography and Calderón's problem (2009, background): “1 has been extended to conductivities having 3/2 derivatives in some sense in [106], [19].”
Inverse Problems for Nonsmooth First Order Perturbations of the Laplacian (2004, background): “Nachman-Sylvester-Uhlmann [27] proved the result for σ ∈W 2,∞, Brown [8] for σ ∈ C3/2+ε using singular zero order perturbations of ∆, Päivärinta-Panchenko-Uhlmann [34] for σ ∈ C3/2 by convolution approximation, and Brown-Torres [10] for σ ∈W 3/2,2n+ε. Uniqueness for C1+ε conormal conductivities wa”
The Calderón Problem with Partial Data for Less Smooth Conductivities (2006, background): “The sharpest uniqueness results so far seem to require essentially 3/2 derivatives of the conductivity to be bounded (Päivärinta et al., 2003) or to be in Lp p > 2n (Brown and Torres, 2003).”