An improved version of a spectral inequality by Payne
arXiv:2507.08631 · doi:10.1016/j.jde.2026.114138
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.