A1 Journal article (refereed)
Inverse problems for real principal type operators (2024)

Oksanen, L., Salo, M., Stefanov, P., & Uhlmann, G. (2024). Inverse problems for real principal type operators. American Journal of Mathematics, 146(1), 161-240. https://doi.org/10.1353/ajm.2024.a917541

JYU authors or editors

Salo, Mikko

Publication details

All authors or editors: Oksanen, Lauri; Salo, Mikko; Stefanov, Plamen; Uhlmann, Gunther

Journal or series: American Journal of Mathematics

ISSN: 0002-9327

eISSN: 1080-6377

Publication year: 2024

Volume: 146

Issue number: 1

Pages range: 161-240

Publisher: Johns Hopkins University Press

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1353/ajm.2024.a917541

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2001.07599

Abstract

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.

Keywords: partial differential equations; inverse problems

Fields of science: