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2014•LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)Open access

Global uniqueness for the Calderón problem with Lipschitz conductivities

Pedro Caro, Keith M. Rogers

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Abstract

We prove uniqueness for Calderón's 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.

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What this paper is about

We prove uniqueness for Calderón's 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.

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Available abstract

We prove uniqueness for Calderón's 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.

Key concepts: Uniqueness, Lipschitz continuity, Conjecture, Mathematics, Identity (music), Work (physics), Pure mathematics, Mathematical analysis

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