Abstract
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.
Citation
Plamen Stefanov. Yang Yang. "The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds." Anal. PDE 11 (6) 1381 - 1414, 2018. https://doi.org/10.2140/apde.2018.11.1381
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