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.
An improved version of a spectral inequality by Payne / Acampora, Paolo; Cristoforoni, Emanuele; Nitsch, Carlo; Trombetti, Cristina. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 461:(2026). [10.1016/j.jde.2026.114138]
An improved version of a spectral inequality by Payne
Paolo Acampora;Emanuele Cristoforoni;Carlo Nitsch;Cristina Trombetti
2026
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
