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

Ghosh, T., Salo, M., & Uhlmann, G. (2020). The Calderón problem for the fractional Schrödinger equation. Analysis and PDE, 13(2), 455-475. https://doi.org/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: https://doi.org/10.2140/apde.2020.13.455

Publication open access: Not open

Publication channel open access: 

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

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Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 3