Estimates for the higher order buckling eigenvalues in the unit sphere

TL;DR

This paper derives universal bounds for higher order buckling eigenvalues of the Dirichlet poly-Laplacian on the unit sphere, improving existing estimates especially for the case p=2.

Contribution

It provides new, sharper bounds for the eigenvalues of the buckling problem that are independent of domain specifics, extending previous results.

Findings

Universal bounds for the (k+1)th eigenvalue in terms of the first k eigenvalues.

Results are independent of domain shape.

For p=2, bounds are sharper than previous estimates.

Abstract

We consider the higher order buckling eigenvalues of the following Dirichlet poly-Laplacian in the unit sphere $(-\Delta)^p u=\Lambda (-\Delta) u$ with order $p(\geq2)$. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the first $k$th eigenvalues independent of the domains. In particular, for $p=2$, our result is sharp than estimates on eigenvalues of the buckling problem obtained by Wang and Xia.