Inverse problems for semilinear elliptic PDE with measurements at a single point
| Authors |
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| Publication date |
05-2023
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| Journal |
Proceedings of the American Mathematical Society
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| Volume | Issue number |
151 | 5
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| Pages (from-to) |
2023-2030
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| Organisations |
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Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
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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.
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| Document type |
Article
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| Language |
English
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| Published at |
https://doi.org/10.1090/proc/16255
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