Analysis & PDE
- Anal. PDE
- Volume 11, Number 6 (2018), 1381-1414.
The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds
We consider the Dirichlet-to-Neumann map on a cylinder-like Lorentzian manifold related to the wave equation related to the metric , the magnetic field and the potential . We show that we can recover the jet of on the boundary from up to a gauge transformation in a stable way. We also show that recovers the following three invariants in a stable way: the lens relation of , and the light ray transforms of and . Moreover, is an FIO away from the diagonal with a canonical relation given by the lens relation. We present applications for recovery of and in a logarithmically stable way in the Minkowski case, and uniqueness with partial data.
Anal. PDE, Volume 11, Number 6 (2018), 1381-1414.
Received: 26 September 2016
Revised: 6 January 2018
Accepted: 14 February 2018
First available in Project Euclid: 23 May 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35R30: Inverse problems
Secondary: 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15] 53B30: Lorentz metrics, indefinite metrics
Stefanov, Plamen; Yang, Yang. The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds. Anal. PDE 11 (2018), no. 6, 1381--1414. doi:10.2140/apde.2018.11.1381. https://projecteuclid.org/euclid.apde/1527040815