Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order

TL;DR

This paper establishes universal bounds for the eigenvalues of the buckling problem of arbitrary order on compact domains, providing bounds that are independent of the specific geometry of the domain.

Contribution

It introduces universal inequalities for eigenvalues of the buckling problem of arbitrary order, applicable to any compact domain in Euclidean spaces and spheres.

Findings

Derived bounds for the kth eigenvalue in terms of lower eigenvalues

Bounds are independent of domain geometry

Applicable to Euclidean spaces and spheres

Abstract

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.