## Mathematics Publications

Mathematics

Article

#### Publication Version

Published Version

1993

#### Journal or Book Title

SIAM Journal on Mathematical Analysis

24

2

327

340

10.1137/0524022

#### Abstract

This paper considers the dependence of the sum of the first m eigenvalues of three classical problems from linear elasticity on a physical parameter in the equation. The paper also considers eigenvalues $\gamma _i (a)$ of a clamped plate under compression, depending on a lateral loading parameter $a;\Lambda i(a)$, the Dirichlet eigenvalues of the elliptic system describing linear elasticity depending on a combination a of the Lame constants, and eigenvalues $\Gamma _i (a)$ of a clamped vibrating plate under tension, depending on the ratio a of tension and flexural rigidity. In all three cases $a \in [0,\infty )$. The analysis of these eigenvalues and their dependence on a gives rise to some general considerations on singularly perturbed variational problems.

This is an article from SIAM Journal on Mathematical Analysis 24 (1993): 327, doi:10.1137/0524022. Posted with permission.

Society for Industrial and Applied Mathematics

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