Year: 2026
Type: preprint
Abstract: We consider an inverse boundary value problem for the time-independent Schrödinger equation in dimension three. We prove that the local Dirichlet-to-Neumann map defined near a boundary point uniquely determines the potential in a neighborhood of the boundary point in the interior. In particular, we show that the uniqueness question can be reduced to the injectivity of a weighted X-ray transform, which links inverse boundary value problems to integral geometry.
Source: arXiv (Cornell University)
Authors: Uhlmann, Gunther, Wang, Yiran
Institutions: University of Washington, Emory University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7164158958