A1 Journal article (refereed)
The Calderón problem for the fractional Schrödinger equation with drift (2020)
Cekić, Mihajlo; Lin, Yi-Hsuan; Rüland, Angkana (2020). The Calderón problem for the fractional Schrödinger equation with drift. Calculus of Variations and Partial Differential Equations, 59 (3), 91. DOI: 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
Open Access: Open access publication published in a hybrid 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
Contributing organizations
Related projects
- Inverse boundary problems: toward a unified theory
- Salo, Mikko
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2020
Preliminary JUFO rating: 2