GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES

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 Habe...

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Bibliographic Details
Published in:Forum of mathematics. Pi 2016, Vol.4, Article e2
Main Authors: CARO, PEDRO, ROGERS, KEITH M.
Format: Article
Language:English
Subjects:
35R30
Differential Equations
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Summary: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.
ISSN:2050-5086
2050-5086
DOI:10.1017/fmp.2015.9