Characterization for stability in planar conductivities

Abstract

We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calderón 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.

44 pages, 1 figure

References in corpus (3)

• Global uniqueness for the Calderón problem with Lipschitz conductivities
• Uniqueness in Calderón's problem for conductivities with unbounded gradient
• Sharp bounds for composition with quasiconformal mappings in Sobolev spaces