On the Ratio of Consecutive Eigenvalues in N‐Dimensions
Colin J. Thompson · Studies in Applied Mathematics · 1969
It is proved that λ2 ≤ (1 + 4/N)λ1 where λ1 ≤ λ2 ≤ ··· are the eigenvalues of the N‐dimensional Laplace operator in a domain D with vanishing boundary conditions. This extends the N = 2 case of Payne, Pólya and Weinberger and the result is independent of the domain D.