Inequalities for Eigenvalues of the Buckling Problem of Higher Orders

TL;DR

This paper establishes universal bounds for eigenvalues in higher-order buckling problems on compact domains, extending previous estimates and providing new inequalities independent of domain specifics.

Contribution

It generalizes existing eigenvalue bounds from second order to arbitrary order for buckling problems, strengthening and broadening prior results.

Findings

Universal bounds for the k-th eigenvalue independent of domain

Extension of Cheng-Yang's estimates to higher orders

Strengthened inequalities for buckling eigenvalues

Abstract

This paper studies eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We prove universal bounds for the $k$-th eigenvalue in terms of the lower ones independent of the domains. Our results strengthens the recent work by Jost, Li-Jost, Wang and Xia and generalizes Cheng-Yang's recent estimates on the buckling eigenvalues of order two to arbitrary order.