Inverse problems for semilinear elliptic PDE with measurements at a single point
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- by Mikko Salo and Leo Tzou
- Proc. Amer. Math. Soc. 151 (2023), 2023-2030
- DOI: https://doi.org/10.1090/proc/16255
- Published electronically: February 10, 2023
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Abstract:
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.References
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Bibliographic Information
- Mikko Salo
- Affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, Jyvaskyla, Finland
- MR Author ID: 749335
- ORCID: 0000-0002-3681-6779
- Email: mikko.j.salo@jyu.fi
- Leo Tzou
- Affiliation: Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, Netherlands
- MR Author ID: 746423
- Email: leo.tzou@gmail.com
- Received by editor(s): March 15, 2022
- Received by editor(s) in revised form: August 26, 2022
- Published electronically: February 10, 2023
- Additional Notes: 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.
- Communicated by: Ryan Hynd
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 2023-2030
- MSC (2020): Primary 35R30
- DOI: https://doi.org/10.1090/proc/16255
- MathSciNet review: 4556197