arXiv:math/0405486 Abstract

arXiv:math/0405486 [math.AP]Abstract References Reviews Resources

The Calderón problem with partial data

Published 2004-05-26, updated 2005-09-14Version 3

In this paper we improve an earlier result by Bukhgeim and Uhlmann, by showing that in dimension larger than or equal to three, the knowledge of the Cauchy data for the Schr\"odinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of Bukhgeim and Uhlmann but use a richer set of solutions to the Dirichlet problem.

Comments: Revised version (Nov 5, 2004) fixing a mistake in section 6 and adding an application to the original problem for the conductivity. Revised version (Sept 14, 2005) modifying a few lines in the introduction and correcting the formula (1.8)

Categories: math.AP

Subjects: 35R30

Keywords: partial data, calderón problem, richer set, general strategy, earlier result

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