A1 Journal article (refereed)
Inverse problems for elliptic equations with fractional power type nonlinearities (2022)
Liimatainen, T., Lin, Y.-H., Salo, M., & Tyni, T. (2022). Inverse problems for elliptic equations with fractional power type nonlinearities. Journal of Differential Equations, 306, 189-219. https://doi.org/10.1016/j.jde.2021.10.015
JYU authors or editors
Publication details
All authors or editors: Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu
Journal or series: Journal of Differential Equations
ISSN: 0022-0396
eISSN: 1090-2732
Publication year: 2022
Volume: 306
Pages range: 189-219
Publisher: Elsevier
Publication country: Netherlands
Publication language: English
DOI: https://doi.org/10.1016/j.jde.2021.10.015
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85284
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2012.04944
Abstract
We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. By using a fractional order adaptation of this method, we show that the results of [24], [23] remain valid for general power type nonlinearities.
Keywords: inverse problems; partial differential equations
Free keywords: Inverse boundary value problem; Calderón problem; Partial data; Semilinear elliptic equations; Higher order linearization; Transversally anisotropic manifold
Contributing organizations
Related projects
- Centre of Excellence in Inverse Problems Research
- Salo, Mikko
- Research Council of Finland
- Inverse boundary problems: toward a unified theory
- Salo, Mikko
- Research Council of Finland
Ministry reporting: Yes
VIRTA submission year: 2022
JUFO rating: 2