A1 Journal article (refereed)
An inverse problem for the fractional Schrödinger equation in a magnetic field (2020)

Covi, G. (2020). An inverse problem for the fractional Schrödinger equation in a magnetic field. Inverse Problems, 36(4), Article 045004. https://doi.org/10.1088/1361-6420/ab661a

JYU authors or editors

Publication details

All authors or editors: Covi, Giovanni

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2020

Volume: 36

Issue number: 4

Article number: 045004

Publisher: Institute of Physics

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/ab661a

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67491

Publication is parallel published: https://arxiv.org/abs/1908.11696

Abstract

This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrödinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely many measurements of solutions taken in arbitrary open subsets of the exterior. The proof is based on Alessandrini's identity and the Runge approximation property, thus generalizing some previous works on the fractional Laplacian. Moreover, we show with a simple model that the FMSE relates to a long jump random walk with weights.

Keywords: inverse problems; magnetic fields

Free keywords: Schrödinger equation

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2