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A Schiffer-type inverse obstacle problem for the planar Schrödinger equation with a single measurement

  • Tony Liimatainen
  • Yi-Hsuan Lin
  • Petri Ola
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Abstract

We prove a single measurement uniqueness result for interior sound-soft obstacles in the planar Schrödinger equation with an unknown surrounding potential. For any two configurations with different obstacles, we construct a boundary datum for which the corresponding Neumann measurements differ. The full Dirichlet-to-Neumann map uniquely determines both the obstacle and the potential. The obstacles may have several connected components, and no convexity or analyticity assumptions are imposed. Neither potential is required to be known near the measurement boundary.

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Cite

BibTeXRIS
BibTeX
@misc{liimatainen2026schiffertype,
  title = {{A Schiffer-type inverse obstacle problem for the planar Schrödinger equation with a single measurement}},
  author = {Tony Liimatainen and Yi-Hsuan Lin and Petri Ola},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12206},
  eprint = {2610.12206},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12206},
}
RIS
TY  - UNPB
TI  - A Schiffer-type inverse obstacle problem for the planar Schrödinger equation with a single measurement
AU  - Tony Liimatainen
AU  - Yi-Hsuan Lin
AU  - Petri Ola
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12206
UR  - https://arxiv.org/abs/2610.12206
AB  - We prove a single measurement uniqueness result for interior sound-soft obstacles in the planar Schrödinger equation with an unknown surrounding potential. For any two configurations with different obstacles, we construct a boundary datum for which the corresponding Neumann measurements differ. The full Dirichlet-to-Neumann map uniquely determines both the obstacle and the potential. The obstacles may have several connected components, and no convexity or analyticity assumptions are imposed. Neither potential is required to be known near the measurement boundary.
ER  -