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


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Publication details

All authors or editorsLiimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu

Journal or seriesJournal of Differential Equations

ISSN0022-0396

eISSN1090-2732

Publication year2022

Volume306

Pages range189-219

PublisherElsevier

Publication countryNetherlands

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.jde.2021.10.015

Publication open accessNot 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.


Keywordsinverse problemspartial differential equations

Free keywordsInverse boundary value problem; Calderón problem; Partial data; Semilinear elliptic equations; Higher order linearization; Transversally anisotropic manifold


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Ministry reportingYes

VIRTA submission year2022

JUFO rating2


Last updated on 2024-12-10 at 12:00