The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds
Plamen StefanovDepartment of Mathematics, Purdue University, West Lafayette, IN, United StatesYang YangDepartment of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, United States
2018en
ABI
Abstract
We consider the Dirichlet-to-Neumann map [math] on a cylinder-like Lorentzian manifold related to the wave equation related to the metric [math] , the magnetic field [math] and the potential [math] . We show that we can recover the jet of [math] on the boundary from [math] up to a gauge transformation in a stable way. We also show that [math] recovers the following three invariants in a stable way: the lens relation of [math] , and the light ray transforms of [math] and [math] . Moreover, [math] is an FIO away from the diagonal with a canonical relation given by the lens relation. We present applications for recovery of [math] and [math] in a logarithmically stable way in the Minkowski case, and uniqueness with partial data.
Identifiers
Citations and references
Cited by 20 references