The buckling eigenvalue problem in the annulus

TL;DR

This paper investigates the buckling eigenvalue problem for a clamped plate in an annulus, analyzing how the first eigenvalue varies with the inner radius and studying eigenfunction nodal domains, including asymptotic behavior.

Contribution

It provides a detailed analysis of the first buckling eigenvalue's dependence on the inner radius and explores eigenfunction nodal domains and asymptotics in related geometries.

Findings

First eigenvalue depends on the inner radius

Number of nodal domains varies with parameters

Asymptotic behavior studied in rectangles

Abstract

We consider the buckling eigenvalue problem for a clamped plate in the annulus. We identify the first eigenvalue in dependence of the inner radius, and study the number of nodal domains of the corresponding eigenfunctions. Moreover, in order to investigate the asymptotic behavior of eigenvalues and eigenfunctions as the inner radius approaches the outer one, we provide an analytical study of the buckling problem in rectangles with mixed boundary conditions.