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. https://doi.org/10.1007/s00208-019-01818-3

JYU authors or editors

Salo, Mikko

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: https://doi.org/10.1007/s00208-019-01818-3

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/72680

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

Fields of science: