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## 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.Comment: 14 page

Topics: Mathematics - Differential Geometry, 35P15, 58C40
Year: 2011
OAI identifier: oai:arXiv.org:1104.5298