Using spherical harmonics, rearrangement techniques, the Sobolev inequality, and Chiti's reverse Hölder inequality, we obtain extensions of a classical result of Payne, Polya, and Weinberger bounding the gap between consecutive eigenvalues of the Dirichlet Laplacian in terms of moments of the preceding ones. The extensions yield domain-dependent inequalities.
- Dirichlet eigenvalue problem for domains in euclidean space
- Domain-dependent inequalities for eigen-values
- Eigenvalues ot the laplacian
- H.C. Yang inequality
- Hile-protter inequality
- Payne-pólya-weinberger inequality
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