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arXiv · 1803.06931

Note on Calder\'on's inverse problem for measurable conductivities

Matteo Santacesaria
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Abstract

The unique determination of a measurable conductivity from the Dirichlet-to-Neumann map of the equation $\mathrm{div} (\sigma \nabla u) = 0$ 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 Calder\'on problem in three and higher dimensions in the $L^\infty$ case.

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Matteo Santacesaria. 2018-03-19. Note on Calder\'on's inverse problem for measurable conductivities. https://doi.org/10.3934/ipi.2019008

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