The Payne conjecture for Dirichlet and Buckling eigenvalues

2021/09/06 by Genqian Liu, Liu, Genqian · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in engineering #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2109.02561

openalex publication_date 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the long-standing Payne conjecture that the k^th eigenvalue in the buckling problem for a clamped plate is not less than the k+1^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≥ 2).

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