The Poisson embedding approach to the Calderón problem
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
Published inMathematische Annalen
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© The Author(s) 2019
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.
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Academy Project, AoF; Centre of Excellence, AoF; FP7 (EU's 7th Framework Programme)
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingOpen access funding provided by University of Jyväskylä (JYU). M.L., T.L. and M.S. were supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963). M.S. was also partly supported by the European Research Council under FP7/2007-2013 (ERC StG 307023) and Horizon 2020 (ERC CoG 770924). We would like to thank an anonymous referee for valuable comments. ...
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