Hadamard’s Variational Formula for Simple Eigenvalues

Here, 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 a two-dimensional domain, which implies several new inequal...

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Bibliographic Details
Published in:AppliedMath 2024-12, Vol.4 (4), p.1211-1229
Main Authors: Suzuki, Takashi, Tsuchiya, Takuya
Format: Article
Language:English
Subjects:
domain deformation
eigenvalue problem
Garabadian–Schiffer’s formula
Hadamard’s variational formula
perturbation theory of linear operators
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Summary:Here, 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 a two-dimensional domain, which implies several new inequalities.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4040065