A1 Journal article (refereed)
The Calderón problem for the fractional Schrödinger equation with drift (2020)

Cekić, M., Lin, Y.-H., & Rüland, A. (2020). The Calderón problem for the fractional Schrödinger equation with drift. Calculus of Variations and Partial Differential Equations, 59(3), Article 91. https://doi.org/10.1007/s00526-020-01740-6

JYU authors or editors

Publication details

All authors or editors: Cekić, Mihajlo; Lin, Yi-Hsuan; Rüland, Angkana

Journal or series: Calculus of Variations and Partial Differential Equations

ISSN: 0944-2669

eISSN: 1432-0835

Publication year: 2020

Volume: 59

Issue number: 3

Article number: 91

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00526-020-01740-6

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/69010

Publication is parallel published: https://jupiter.math.nctu.edu.tw/~yihsuanlin3/papers/fractional_drift_v23.pdf

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1810.04211

Abstract

We investigate the Calderón problem for the fractional Schrödinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does not enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many generic measurements is discussed. Here the genericity is obtained through singularity theory which might also be interesting in the context of hybrid inverse problems. Combined with the results from Ghosh et al. (Uniqueness and reconstruction for the fractional Calderón problem with a single easurement, 2018. arXiv:1801.04449), this yields a finite measurements constructive reconstruction algorithm for the fractional Calderón problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension n≥ 1.

Keywords: inverse problems; partial differential equations

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2