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
Published inProceedings of the American Mathematical Society
DisciplineInversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematics
©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.
PublisherAmerican Mathematical Society (AMS)
ISSN Search the Publication Forum0002-9939
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland; European Commission
Funding program(s)Centre of Excellence, AoF
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 fundingThe 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.
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