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

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arxiv 2202.05290 v2 pith:EFJSKB4U submitted 2022-02-10 math.AP

Mikko Salo , Leo Tzou This is my paper
classification math.AP
keywords boundarydirichlet-to-neumannellipticinversepointpotentialsemilinearsingle
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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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  1. Partial data Calder\'{o}n problem for quasilinear conductivities in dimension 2

    math.AP 2026-07 conditional novelty 6.0 of 10

    Partial boundary measurements uniquely determine a quasilinear two-dimensional conductivity γ(x,u,∇u) without restricting the gradient dependence.

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