A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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-tekijät tai -toimittajat
Julkaisun tiedot
Julkaisun kaikki tekijät tai toimittajat: Cekić, Mihajlo; Lin, Yi-Hsuan; Rüland, Angkana
Lehti tai sarja: Calculus of Variations and Partial Differential Equations
ISSN: 0944-2669
eISSN: 1432-0835
Julkaisuvuosi: 2020
Volyymi: 59
Lehden numero: 3
Artikkelinumero: 91
Kustantaja: Springer
Julkaisumaa: Saksa
Julkaisun kieli: englanti
DOI: https://doi.org/10.1007/s00526-020-01740-6
Julkaisun avoin saatavuus: Avoimesti saatavilla
Julkaisukanavan avoin saatavuus: Osittain avoin julkaisukanava
Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/69010
Julkaisu on rinnakkaistallennettu: https://jupiter.math.nctu.edu.tw/~yihsuanlin3/papers/fractional_drift_v23.pdf
Rinnakkaistallenteen verkko-osoite (pre-print): https://arxiv.org/abs/1810.04211
Tiivistelmä
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.
YSO-asiasanat: inversio-ongelmat; osittaisdifferentiaaliyhtälöt
Liittyvät organisaatiot
Hankkeet, joissa julkaisu on tehty
- Käänteisten reuna-arvo-ongelmien teoria
- Salo, Mikko
- Suomen Akatemia
OKM-raportointi: Kyllä
Raportointivuosi: 2020
JUFO-taso: 2