Note on Calderón's inverse problem for measurable conductivities

Matteo Santacesaria

doi:10.3934/ipi.2019008

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2019, Volume 13, Issue 1: 149-157. Doi: 10.3934/ipi.2019008

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Note on Calderón's inverse problem for measurable conductivities

Matteo Santacesaria

Department of Mathematics, University of Genoa, Via Dodecaneso 35, 16146 Genova, Italy

Received: January 31, 2018

Revised: May 31, 2018

Published: December 2018

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Abstract

The unique determination of a measurable conductivity from the Dirichlet-to-Neumann map of the equation ${\rm{div}} (σ \nabla u) = 0$ is the subject of this note. A new strategy, based on Clifford algebras and a higher dimensional analogue of the Beltrami equation, is here proposed. This represents a possible first step for a proof of uniqueness for the Calderón problem in three and higher dimensions in the $L^\infty$ case.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 15A66, 35J56.

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References

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