Hadamard variation of eigenvalues with respect to general domain perturbations

Takashi Suzuki; Takuya Tsuchiya

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arXiv · 2309.00273

Hadamard variation of eigenvalues with respect to general domain perturbations

Takashi Suzuki·Takuya Tsuchiya

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Abstract

We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite dimensional spaces. Then smooth rearrangement of multiple eigenvalues is explicitly given. This result follows from an abstract theory, applicable to general perturbations of symmetric bilinear forms.

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Takashi Suzuki, Takuya Tsuchiya. 2023-09-01. Hadamard variation of eigenvalues with respect to general domain perturbations. https://arxiv.org/abs/2309.00273

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