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PreprintCC BY-NC-SA 4.0arXiv

Payne's conjecture for buckling eigenvalues of odd index

  • Michael Levitin
  • Iosif Polterovich
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Abstract

In 1955, L. E. Payne conjectured that for a planar clamped plate, each buckling eigenvalue is at least as large as the Dirichlet Laplacian eigenvalue of the same domain with index shifted by one. We prove this conjecture for every odd buckling index.

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Cite

BibTeXRIS
BibTeX
@misc{levitin2026paynes,
  title = {{Payne's conjecture for buckling eigenvalues of odd index}},
  author = {Michael Levitin and Iosif Polterovich},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12235},
  eprint = {2609.12235},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12235},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Payne's conjecture for buckling eigenvalues of odd index
AU  - Michael Levitin
AU  - Iosif Polterovich
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.12235
UR  - https://arxiv.org/abs/2609.12235
AB  - In 1955, L. E. Payne conjectured that for a planar clamped plate, each buckling eigenvalue is at least as large as the Dirichlet Laplacian eigenvalue of the same domain with index shifted by one. We prove this conjecture for every odd buckling index.
ER  -