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Hadamard’ Variational Formula for Simple Eigenvalues
Version 1
: Received: 28 August 2024 / Approved: 28 August 2024 / Online: 28 August 2024 (10:39:38 CEST)
How to cite: Suzuki, T.; Tsuchiya, T. Hadamard’ Variational Formula for Simple Eigenvalues. Preprints 2024, 2024082005. https://doi.org/10.20944/preprints202408.2005.v1 Suzuki, T.; Tsuchiya, T. Hadamard’ Variational Formula for Simple Eigenvalues. Preprints 2024, 2024082005. https://doi.org/10.20944/preprints202408.2005.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.
Keywords
eigenvalue problem; perturbation theory of linear operators; domain deformation; Hadamard's variational formula; Garabadian-Schiffer's formula
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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