Work

Boundary rigidity with partial data

Year: 2013

Type: preprint

Abstract: We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the boundary. We show that one can recover uniquely and in a stable way a conformal factor near a strictly convex point where we have the information. In particular, this implies that we can determine locally the isotropic sound speed of a medium by measuring the travel times of waves joining points close to a convex point on the boundary. The local results lead to a global lens rigidity uniqueness and stability result assuming that the manifold is foliated by strictly convex hypersurfaces.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1306.2995

Authors: Stefanov, Plamen, Uhlmann, Gunther, Vasy, Andras

Institutions: Purdue University West Lafayette, University of Helsinki, University of Washington, Stanford University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Inverse Problems for Wave Phenomena, Propagation Phenomena for Waves and Scattering, CMG: Nonlinear Elastic-Wave Inverse Scattering and Tomography - from Cracks to Mantle Convection, Inverse Boundary Problems

OpenAlex ID: W2952720941

Cites: 31

Cited by: 8

Related to: 20