Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities

Albert Clop; Daniel Faraco; Alberto Ruiz

doi:10.3934/ipi.2010.4.49

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2010, Volume 4, Issue 1: 49-91. Doi: 10.3934/ipi.2010.4.49

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Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities

1.
Department of Mathematics and Statistics, P.O.Box 35 (MaD), FI-40014 University of Jyväskylä
2.
Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UC3M and Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049-Madrid
3.
Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049-Madrid

Received: June 30, 2008

Revised: October 31, 2009

Published: January 2010

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Abstract

It is proved that, in two dimensions, the Calderón inverse conductivity problem in Lipschitz domains is stable in the $L^p$ sense when the conductivities are uniformly bounded in any fractional Sobolev space $W^{\alpha,p}$ $\alpha>0, 1 < p < \infty$.

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Mathematics Subject Classification: 35R30, 35J15, 30C62.

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Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities

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