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Hadamard's variational formula for simple eigenvalues

Analysis of PDEs 2024-09-09 v1

Abstract

We study Hadamard's variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for two-dimensional domain, which implies several new inequalities.

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Cite

@article{arxiv.2409.04021,
  title  = {Hadamard's variational formula for simple eigenvalues},
  author = {Takashi Suzuki and Takuya Tsuchiya},
  journal= {arXiv preprint arXiv:2409.04021},
  year   = {2024}
}

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submitted

R2 v1 2026-06-28T18:36:06.374Z