A1 Journal article (refereed)
Inverse problems for elliptic equations with power type nonlinearities (2021)


Lassas, M., Liimatainen, T., Lin, Y.-H., & Salo, M. (2021). Inverse problems for elliptic equations with power type nonlinearities. Journal de Mathematiques Pures et Appliquees, 145, 44-82. https://doi.org/10.1016/j.matpur.2020.11.006


JYU authors or editors


Publication details

All authors or editors: Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko

Journal or series: Journal de Mathematiques Pures et Appliquees

ISSN: 0021-7824

eISSN: 1776-3371

Publication year: 2021

Volume: 145

Pages range: 44-82

Publisher: Elsevier

Publication country: France

Publication language: English

DOI: https://doi.org/10.1016/j.matpur.2020.11.006

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/73381

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1903.12562


Abstract

We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension 2, and a potential on transversally anisotropic manifolds in dimensions . In the Euclidean case, we show that one can solve the Calderón problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions.


Keywords: inverse problems; partial differential equations

Free keywords: inverse boundary value problem; Calderón problem; semilinear equation; transversally anisotropic


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Ministry reporting: Yes

Reporting Year: 2021

Preliminary JUFO rating: 3


Last updated on 2021-07-07 at 17:54