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


Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther (2020). The Calderón problem for the fractional Schrödinger equation. Analysis and PDE, 13 (2), 455-475. DOI: 10.2140/apde.2020.13.455


JYU authors or editors


Publication details

All authors or editors: Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther

Journal or series: Analysis and PDE

ISSN: 2157-5045

eISSN: 1948-206X

Publication year: 2020

Volume: 13

Issue number: 2

Pages range: 455-475

Publisher: Mathematical Sciences Publishers

Publication country: United States

Publication language: English

DOI: http://doi.org/10.2140/apde.2020.13.455

Open Access: Publication channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68259

Publication is parallel published: https://arxiv.org/abs/1609.09248


Abstract

We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension ≥1 and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calderón problem.


Keywords: inverse problems; partial differential equations; approximation

Free keywords: inverse problem; Calderón problem; fractional Laplacian; approximation property


Contributing organizations


Related projects

Centre of Excellence in Inverse Problems Research
Salo, Mikko
Academy of Finland
01/01/2015-31/12/2017
Inverse boundary problems: toward a unified theory
Salo, Mikko
Academy of Finland
01/09/2017-31/08/2021
Inverse boundary problems - toward a unified theory
Salo, Mikko
European Commission
01/05/2018-30/04/2023


Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 3


Last updated on 2020-18-08 at 13:03