Bounds for eigenvalue ratios of the Laplacian

Details Bounds for eigenvalue ratios of the Laplacian Bounds for eigenvalue ratios of the Laplacian

2011-04-28

arxiv.org/abs/1104.5298v2

Mathematics

Differential Geometry

14 pages

Scientific paper

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.

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