## Global uniqueness from partial Cauchy data in two dimensions. Arxiv preprint arXiv:0810.2286 (2008)

Citations: | 12 - 1 self |

### BibTeX

@MISC{Imanuvilov08globaluniqueness,

author = {Oleg Yu. Imanuvilov and Gunther Uhlmann and Masahiro Yamamoto},

title = {Global uniqueness from partial Cauchy data in two dimensions. Arxiv preprint arXiv:0810.2286},

year = {2008}

}

### OpenURL

### Abstract

Abstract. We prove for a two dimensional bounded domain that the Cauchy data for the Schrödinger 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. 1.