Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform

2000/01/18 by Allan Greenleaf, Gunther Uhlmann, Günther Uhlmann +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35R30 #44A12 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #math-ph #math.AP #math.MP #msc:35R30 #msc:44A12

paper · pdf · doi:10.48550/arxiv.math/0001099

Final revision, to appear in the Duke Mathmematical Journal

openalex publication_date 2000/01/18 · arxiv created 2000/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Dirichlet-to-Neumann map associated to the Schrödinger 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.

Citations

• Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Related

• Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions
• Inverse boundary value problem for linear Schrödinger equation in two dimensions
• The Square of the Dirichlet-to-Neumann map equals minus Laplacian
• Partial Data for the Neumann-to-Dirichlet Map
• Uniqueness of a Potential from Local Boundary Measurements