Payne's conjecture for buckling eigenvalues of odd index

Abstract

In 1955, L. E. Payne conjectured that for a planar clamped plate, each buckling eigenvalue is at least as large as the Dirichlet Laplacian eigenvalue of the same domain with index shifted by one. We prove this conjecture for every odd buckling index.

v2: minor revisions; 9 pages