Bounds for eigenvalue ratios of the Laplacian


For a bounded domain Ω\Omega with a piecewise smooth boundary in an nn-dimensional Euclidean space Rn\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

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