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

OKM-raportointi: Kyllä

Raportointivuosi: 2020

JUFO-taso: 2