Global uniqueness from partial Cauchy data in two dimensions

Details Global uniqueness from partial Cauchy data in two dimensions Global uniqueness from partial Cauchy data in two dimensions

2008-10-13

arxiv.org/abs/0810.2286v1

Mathematics

Analysis of PDEs

Scientific paper

We prove for a two dimensional bounded domain that the Cauchy data for the Schroedinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential. This implies, for the conductivity equation, that if we measure the current fluxes at the boundary on an arbitrary open subset of the boundary produced by voltage potentials supported in the same subset, we can determine uniquely the conductivity. We use Carleman estimates with degenerate weight functions to construct appropriate complex geometrical optics solutions to prove the results.

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