On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary

Gennadi Henkin; Roman Novikov

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arXiv · 1003.4897

On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary

Gennadi Henkin·Roman Novikov

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Abstract

An electrical potential U on bordered surface X (in Euclidien three-dimensional space) with isotropic conductivity function sigma>0 satisfies equation d(sigma d^cU)=0, where d^c is real operator associated with complex (conforme) structure on X induced by Euclidien metric of three-dimensional space. This paper gives exact reconstruction of conductivity function sigma on X from Dirichlet-to-Neumann mapping (for aforementioned conductivity equation) on the boundary of X. This paper extends to the case of the Riemann surfaces the reconstruction schemes of R.Novikov (1988) and of A.Bukhgeim (2008) given for the case of domains in two-dimensional Euclidien space. The paper extends and corrects the statements of Henkin-Michel (2008), where the inverse boundary value problem on the Riemann surfaces was firstly considered.

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Gennadi Henkin, Roman Novikov. 2010-03-25. On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary. https://arxiv.org/abs/1003.4897

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