An improved version of a spectral inequality by Payne
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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Journal of Differential Equations
- Volume
- 461
- Pages
- 114138–114138
- Publication date
- 28 January 2026
- Language
- EN