A1 Journal article (refereed)
The Fixed Angle Scattering Problem with a First-Order Perturbation (2021)
Meroño, C. J., Potenciano-Machado, L., & Salo, M. (2021). The Fixed Angle Scattering Problem with a First-Order Perturbation. Annales Henri Poincaré : a journal of theoretical and mathematical physics, 22(11), 3699-3746. https://doi.org/10.1007/s00023-021-01081-w
JYU authors or editors
Publication details
All authors or editors: Meroño, Cristóbal J.; Potenciano-Machado, Leyter; Salo, Mikko
Journal or series: Annales Henri Poincaré : a journal of theoretical and mathematical physics
ISSN: 1424-0637
eISSN: 1424-0661
Publication year: 2021
Publication date: 05/07/2021
Volume: 22
Issue number: 11
Pages range: 3699-3746
Publisher: Springer Science and Business Media LLC
Publication country: Switzerland
Publication language: English
DOI: https://doi.org/10.1007/s00023-021-01081-w
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/77068
Abstract
We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by 2n measurements up to a natural gauge. We also show that one can recover the full first-order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and Salo (SIAM J Math Anal 52(6):5467–5499, 2020) and (Inverse Probl 36(3):035005, 2020) to Hamiltonians with first-order perturbations, and it is based on wave equation methods and Carleman estimates.
Keywords: inverse problems
Free keywords: inverse scattering problems
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 1