The Fixed Angle Scattering Problem with a First-Order Perturbation
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
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2021 The Author(s)
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.
PublisherSpringer Science and Business Media LLC
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Additional information about fundingOpen access funding provided by University of Jyväskylä (JYU).
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