Hadamard's variational formula for simple eigenvalues

Takashi Suzuki; Takuya Tsuchiya

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arXiv · 2409.04021

Hadamard's variational formula for simple eigenvalues

Takashi Suzuki·Takuya Tsuchiya

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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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Takashi Suzuki, Takuya Tsuchiya. 2024-09-06. Hadamard's variational formula for simple eigenvalues. https://arxiv.org/abs/2409.04021

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