A partial data result for less regular conductivities in admissible geometries
Analysis of PDEs
2016-02-16 v2
Abstract
We consider the Calder\'on problem with partial data in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. We show that measuring the Dirichlet-to-Neumann map on roughly half of the boundary determines a conductivity that has essentially 3/2 derivatives. As a corollary, we strengthen a partial data result due to Kenig, Sj\"ostrand, and Uhlmann.
Cite
@article{arxiv.1412.1387,
title = {A partial data result for less regular conductivities in admissible geometries},
author = {Casey Rodriguez},
journal= {arXiv preprint arXiv:1412.1387},
year = {2016}
}
Comments
15 pages, 1 appendix, minor corrections, to appear in Inverse Problems and Imaging