Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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