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

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Related projects

Ministry reporting: Yes

VIRTA submission year: 2022

JUFO rating: 2