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