Estimates on the first two buckling eigenvalues on spherical domains

TL;DR

This paper provides improved estimates for the first two buckling eigenvalues on spherical domains, advancing understanding of their relationship and refining previous bounds.

Contribution

It introduces a new estimate for the second eigenvalue based on the first, improving upon recent results by Wang-Xia.

Findings

Enhanced bounds for the second eigenvalue in terms of the first

Refined estimates improve previous results by Wang-Xia

Contributes to spectral theory of buckling problems on spheres

Abstract

In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].