Inverse problems for semilinear elliptic PDE with measurements at a single point

Mikko Salo; Leo Tzou

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arXiv · 2202.05290

Inverse problems for semilinear elliptic PDE with measurements at a single point

Mikko Salo·Leo Tzou

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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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Mikko Salo, Leo Tzou. 2022-02-10. Inverse problems for semilinear elliptic PDE with measurements at a single point. https://arxiv.org/abs/2202.05290

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