Note on Calderón's inverse problem for measurable conductivities

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 Calderón problem in three and higher dimensions in the $L^{\infty }$ case.

11 pages