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arXiv · 2507.08631

An improved version of a spectral inequality by Payne

Paolo Acampora·Emanuele Cristoforoni·Carlo Nitsch·Cristina Trombetti
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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.

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Paolo Acampora, Emanuele Cristoforoni, Carlo Nitsch, Cristina Trombetti. 2025-07-11. An improved version of a spectral inequality by Payne. https://doi.org/10.1016/j.jde.2026.114138

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