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. https://doi.org/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: https://doi.org/10.1016/j.na.2019.05.010
Publication open access: Not open
Publication channel open access:
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
- Research Council of Finland
- InvProbGeomPDE Inverse Problems in Partial Differential Equations and Geometry
- Salo, Mikko
- European Commission
- Inverse boundary problems - toward a unified theory
- Salo, Mikko
- European Commission
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 1