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Note on Calderón's inverse problem for measurable conductivities

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  • 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.

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


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