Hadamard's Variational Formula for Simple Eigenvalues

被引：0

作者：

Suzuki, Takashi ^{[1
]}

Tsuchiya, Takuya ^{[1
]}

机构：

[1] Osaka Univ, Ctr Math Modeling & Data Sci, Osaka 5650871, Japan

来源：

APPLIEDMATH | 2024年 / 4卷 / 04期

关键词：

eigenvalue problem; perturbation theory of linear operators; domain deformation; Hadamard's variational formula; Garabadian-Schiffer's formula;

D O I：

10.3390/appliedmath4040065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1211 / 1229

页数：19

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