Inverse problems for semilinear elliptic PDE with measurements at a single point
Salo, M., & Tzou, L. (2023). Inverse problems for semilinear elliptic PDE with measurements at a single point. Proceedings of the American Mathematical Society, 151(5), 2023-2030. https://doi.org/10.1090/proc/16255
Julkaistu sarjassa
Proceedings of the American Mathematical SocietyPäivämäärä
2023Oppiaine
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsTekijänoikeudet
©2023 American Mathematical Society
We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neumann map measured at a single boundary point, or integrated against a fixed measure. This result is valid even when the Dirichlet data is only given on a small subset of the boundary. We also give related uniqueness results on Riemannian manifolds.
Julkaisija
American Mathematical Society (AMS)ISSN Hae Julkaisufoorumista
0002-9939Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/177819392
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen Akatemia; Euroopan komissioRahoitusohjelmat(t)
Huippuyksikkörahoitus, SA
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.
Lisätietoja rahoituksesta
The first author was partly supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant 284715) and by the European Research Council under Horizon 2020 (ERC CoG 770924). The second author was partly supported by Australian Research Council Discovery Projects DP190103451 and DP190103302.Lisenssi
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