A1 Journal article (refereed)
The fractional Calderón problem : Low regularity and stability (2020)


Rüland, A., & Salo, M. (2020). The fractional Calderón problem : Low regularity and stability. Nonlinear Analysis: Theory, Methods and Applications, 193, 111529. doi:10.1016/j.na.2019.05.010


JYU authors or editors


Publication details

All authors or editors: Rüland, Angkana; Salo, Mikko

Journal or series: Nonlinear Analysis: Theory, Methods and Applications

ISSN: 0362-546X

eISSN: 1873-5215

Publication year: 2020

Volume: 193

Issue number: 0

Pages range: 111529

Publisher: Elsevier

Publication country: United Kingdom

Publication language: English

DOI: http://doi.org/10.1016/j.na.2019.05.010

Open Access: Publication channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67898

Publication is parallel published: https://arxiv.org/abs/1708.06294


Abstract

The Calderón problem for the fractional Schrödinger equation was introduced in the work Ghosh et al. (to appear)which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant Lp or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli–Silvestre extension and a duality argument.


Keywords: inverse problems; partial differential equations

Free keywords: Caldernón problem; fractional Laplacian; stability


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
European Commission
01/05/2018-30/04/2023


Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 1


Last updated on 2020-18-10 at 21:45