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Improving a Spectral Inequality by Payne

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GSTW02 - Geometry of eigenvalues

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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