PreprintCC BY 4.0arXiv
Stability for a formally determined Lorentzian inverse problem
Abstract
We consider the inverse problem of recovering a potential q, depending on space and time, in the wave equation (Boxg+q)u=0 on a Lorentzian manifold. We prove Lipschitz stability for a formally determined version of this problem under a \textit{null-cone foliation} assumption. As a consequence, we obtain uniqueness for the Lorentzian Calderón problem in a fixed conformal class. Our approach uses distorted spherical waves.
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BibTeX
@misc{filippas2026stability,
title = {{Stability for a formally determined Lorentzian inverse problem}},
author = {Spyridon Filippas and Lauri Oksanen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10413},
eprint = {2610.10413},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10413},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability for a formally determined Lorentzian inverse problem
AU - Spyridon Filippas
AU - Lauri Oksanen
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.10413
UR - https://arxiv.org/abs/2610.10413
AB - We consider the inverse problem of recovering a potential q, depending on space and time, in the wave equation (Box_g+q)u=0 on a Lorentzian manifold. We prove Lipschitz stability for a formally determined version of this problem under a \textit{null-cone foliation} assumption. As a consequence, we obtain uniqueness for the Lorentzian Calderón problem in a fixed conformal class. Our approach uses distorted spherical waves.
ER -