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arXiv · 1701.06480

Characterization for stability in planar conductivities

Daniel Faraco·Martí Prats
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Abstract

We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calder\'on Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are constant in a neighborhood of its boundary. To obtain this result, we present minimal a priori assumptions which turn to be sufficient for sets of conductivities to have stable recovery in a bounded and rough domain. The condition is presented in terms of the modulus of continuity of the coefficients involved and their ellipticity bound.

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Daniel Faraco, Martí Prats. 2017-01-23. Characterization for stability in planar conductivities. https://doi.org/10.1016/j.jde.2018.01.013

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