The Calder\'on problem with partial data
Analysis of PDEs
2007-05-23 v3
Abstract
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.
Cite
@article{arxiv.math/0405486,
title = {The Calder\'on problem with partial data},
author = {C. E. Kenig and J. Sjoestrand and G. Uhlmann},
journal= {arXiv preprint arXiv:math/0405486},
year = {2007}
}
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)