Inverse problems for semilinear elliptic PDE with measurements at a single point
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| Publication date | 05-2023 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | Issue number | 151 | 5 |
| Pages (from-to) | 2023-2030 |
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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. |
| Document type | Article |
| Language | English |
| Published at |
https://doi.org/10.1090/proc/16255
(Final published version)
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