Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform
Analysis of PDEs
2007-05-23 v4 Mathematical Physics
math.MP
Abstract
We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potential over a two-plane is determined by the Cauchy data of certain exponentially growing solutions on any neighborhood of the intersection of the two-plane with the boundary.
Cite
@article{arxiv.math/0001099,
title = {Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform},
author = {Allan Greenleaf and Gunther Uhlmann},
journal= {arXiv preprint arXiv:math/0001099},
year = {2007}
}
Comments
Final revision, to appear in the Duke Mathmematical Journal