The Payne conjecture for Dirichlet and Buckling eigenvalues

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 ($n\ge 2)$.

There exists an error in the proof of Lemma 4.2

Cited by in corpus (1)

• On the paper "The Payne conjecture for Dirichlet and buckling eigenvalues", by Genquian Liu