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arXiv · 2606.10247

The partial data Calder\'on problem in dimension three

Gunther Uhlmann·Yiran Wang
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Abstract

We consider an inverse boundary value problem for the time-independent Schr\"odinger equation in dimension three. We prove that the local Dirichlet-to-Neumann map defined near a boundary point uniquely determines the potential in a neighborhood of the boundary point in the interior. In particular, we show that the uniqueness question can be reduced to the injectivity of a weighted X-ray transform, which links inverse boundary value problems to integral geometry.

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Gunther Uhlmann, Yiran Wang. 2026-06-08. The partial data Calder\'on problem in dimension three. https://arxiv.org/abs/2606.10247

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