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.
Funding Statement
This work was promoted in RIMS program for joint research during 2019–2021. The first author was supported by JSPS Grant-in-Aid for Scientific Research 19H01799. The second author was supported by JSPS Grant-in-Aid for Scientific Research 21K03372.
Citation
Takashi SUZUKI. Takuya TSUCHIYA. "Hadamard variation of eigenvalues with respect to general domain perturbations." J. Math. Soc. Japan 76 (4) 1087 - 1122, October, 2024. https://doi.org/10.2969/jmsj/90989098
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