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arXiv · 2109.02561

The Payne conjecture for Dirichlet and Buckling eigenvalues

Genqian Liu
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Abstract

We prove the long-standing Payne conjecture that the $k^{\text{th}}$ eigenvalue in the buckling problem for a clamped plate is not less than the ${k+1}^{\text{st}}$ eigenvalue for the membrane of the same shape which is fixed on the boundary. Moreover, we show that the Payne conjecture is still true for $n$-dimensional case ($n\ge 2)$.

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Genqian Liu. 2021-09-23. The Payne conjecture for Dirichlet and Buckling eigenvalues. https://arxiv.org/abs/2109.02561

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