On the estimate of the gap of the first two eigenvalues of the Laplacian
Zhiqiang Shao · Fuzhou daxue xuebao. Ziran kexue ban · 2002
By means of the maximum principle, the following result is proved: let Ω be a bounded convex domain in R n with smooth boundary, then the gap of the first two eigenvalues of the Laplacian on Ω with Dirichlet boundary condition satisfies: λ\-2-λ\-1≥π\+2d\+2, where d is the diameter of Ω.