Preprint

Inserted: 29 jul 2025
Last Updated: 29 jul 2025

Year: 2025
Doi: https://arxiv.org/abs/2507.08631

Abstract:

A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne’s original estimate—which is not sharp—can in fact be improved. Our result provides a refined spectral bound and opens the way to further investigations into quantitative enhancements of classical inequalities in spectral theory

Keywords: convex sets, Dirichlet eigenvalue, spectral inequalities, Buckling eigenvalue