Characterization for stability in planar conductivities
EntityUAM. Departamento de Matemáticas; Instituto de Ciencias Matemáticas (ICMAT)
10.1016/j.jde.2018.01.013Journal of Differential Equations 264.9 (2018): 5659-5712
Funded byThe authors were funded by the European Research Council under the grant agreement 307179-GFTIPFD and MTM2011-28198 and they acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa" Programme for Centres of Excellence in R&D (SEV-2015-0554). The second author was partially funded by AGAUR - Generalitat de Catalunya (2014 SGR 75) as well
Projectinfo:eu-repo/grantAgreement/EC/FP7/307179; info:eu-repo/grantAgreement/EC/FP7/28198; Gobierno de España. SEV-2015-0554
SubjectsCalderon Inverse Problem; Complex Geometric Optics Solutions; Stability; Quasiconformal mappings; Integral modulus of continuity; Matemáticas
NoteFinal publication at http://doi.org/10.1016/j.jde.2018.01.013, © 2018 Elsevier Inc.
Rights© 2018 Elsevier Inc. All rights reserved.
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
We find a complete characterization for sets of uniformly strongly elliptic and isotropic conductivities with stable recovery in the 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 out 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 integral moduli of continuity of the coefficients involved and their ellipticity bound as conjectured by Alessandrini in his 2007 paper, giving explicit quantitative control for every pair of conductivities
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