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

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February 2010, 4(1): 49-91. doi: 10.3934/ipi.2010.4.49

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

Albert Clop ^1, , Daniel Faraco ^2, and Alberto Ruiz ^3,

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

Received July 2008 Revised November 2009 Published February 2010

Abstract
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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 $W^{\alpha,p}$ $\alpha>0, 1 < p < \infty$.

Keywords: Calderón's problem, Inverse problem, stability.

Mathematics Subject Classification: 35R30, 35J15, 30C6.

Citation: Albert Clop, Daniel Faraco, Alberto Ruiz. Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities. Inverse Problems & Imaging, 2010, 4 (1) : 49-91. doi: 10.3934/ipi.2010.4.49

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