A1 Journal article (refereed)
The Poisson embedding approach to the Calderón problem (2020)


Lassas, M., Liimatainen, T., & Salo, M. (2020). The Poisson embedding approach to the Calderón problem. Mathematische Annalen, 377 (1-2), 19-67. doi:10.1007/s00208-019-01818-3


JYU authors or editors


Publication details

All authors or editors: Lassas, Matti; Liimatainen, Tony; Salo, Mikko

Journal or series: Mathematische Annalen

ISSN: 0025-5831

eISSN: 1432-1807

Publication year: 2020

Volume: 377

Issue number: 1-2

Pages range: 19-67

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: http://doi.org/10.1007/s00208-019-01818-3

Open Access: Open access publication published in a hybrid channel

Web address where publication is available: https://arxiv.org/abs/1806.04954


Abstract

We introduce a new approach to the anisotropic Calderón problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calderón type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result of Lassas et al. (Annales de l’ ENS 34(5):771–787, 2001) solving the Calderón problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.


Keywords: inverse problems; partial differential equations

Free keywords: Calderón problem; Poisson embedding


Contributing organizations

Other organizations:


Related projects

Centre of Excellence in Inverse Problems Research
Salo, Mikko
Academy of Finland
01/01/2015-31/12/2017
Inverse boundary problems: toward a unified theory
Salo, Mikko
Academy of Finland
01/09/2017-31/08/2021
Inverse boundary problems - toward a unified theory
Salo, Mikko
European Commission
01/05/2018-30/04/2023


Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 2


Last updated on 2020-18-10 at 21:25