Hadamard's variational formula for simple eigenvalues

2024/09/06 by Takashi Suzuki, Suzuki, Takashi, Takuya Tsuchiya +1
Computer Science · Engineering · #35J25 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2409.04021

openalex publication_date 2024/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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