Bounds for eigenvalue ratios of the Laplacian

Abstract

For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space ${\mathbf{R}}^n$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Laplacian and derive the ratios of lower order eigenvalues of the Laplacian.

14 pages