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GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  13 January 2016

PEDRO CARO  and
KEITH M. ROGERS
PEDRO CARO
Affiliation:
BCAM - Basque Center for Applied Mathematics, 48009 Bilbao, Spain; pcaro@bcamath.org Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
KEITH M. ROGERS
Affiliation:
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain; keith.rogers@icmat.es

Abstract

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We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three- and four-dimensional cases, this confirms a conjecture of Uhlmann. Our proof builds on the work of Sylvester and Uhlmann, Brown, and Haberman and Tataru who proved uniqueness for $C^{1}$-conductivities and Lipschitz conductivities sufficiently close to the identity.

MSC classification

Primary: 35R30: Inverse problems
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 4 , 2016 , e2
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2016

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