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The partial data Calderón problem in dimension three

  • Gunther Uhlmann
  • Yiran Wang
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Abstract

We consider an inverse boundary value problem for the time-independent Schrödinger 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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Cite

BibTeXRIS
BibTeX
@misc{uhlmann2026partial,
  title = {{The partial data Calderón problem in dimension three}},
  author = {Gunther Uhlmann and Yiran Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.10247},
  eprint = {2606.10247},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.10247},
}
RIS
TY  - UNPB
TI  - The partial data Calderón problem in dimension three
AU  - Gunther Uhlmann
AU  - Yiran Wang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2606.10247
UR  - https://arxiv.org/abs/2606.10247
AB  - We consider an inverse boundary value problem for the time-independent Schrödinger 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.
ER  -