On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics

DOI10.1216/RMJ-2008-38-4-1037zbMath1184.35232MaRDI QIDQ1011047

Lotfi Hermi, Mark S. Ashbaugh

Publication date: 7 April 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

eigenvalues of the LaplacianPayne-Pólya-Weinberger inequalityDirichlet eigenvalue problem for domains in Euclidean spacedomain-dependent inequalities for eigenvaluesH. C. Yang inequalityHileprotter inequality

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spherical harmonics (33C55) Variational methods for eigenvalues of operators (49R05)

Related Items

Isoperimetric inequalities for a wedge-like membrane ⋮ Two new Weyl-type bounds for the Dirichlet Laplacian ⋮ The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H. C. Yang

Cites Work

• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions
• Problèmes isoperimetriques et espaces de Sobolev
• Analysis of spherical symmetries in Euclidean spaces
• The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H. C. Yang
• A unified approach to universal inequalities for eigenvalues of elliptic operators
• A reverse Hölder inequality for the eigenfunctions of linear second order elliptic operators
• Commutators, spectral trace identities, and universal estimates for eigenvalues
• Bounds for the ratios of the first three membrane eigenvalues
• Spherical harmonics
• On the Ratio of Consecutive Eigenvalues
• A Bound for the Ratio of the First Two Eigenvalues of a Membrane
• Domain-Independent Upper Bounds for Eigenvalues of Elliptic Operators
• Proof of the Payne-Pólya-Weinberger conjecture
• Some geometric bounds on eigenvalue gaps
• More Bounds on Eigenvalue Ratios for Dirichlet Laplacians inNDimensions
• Commutator bounds for eigenvalues, with applications to spectralgeometry
• On trace identities and universal eigenvalue estimates for some partial differential operators
• Some Inequalities for the First Positive Zeros of Bessel Functions
• On the Ratio of Consecutive Eigenvalues in N‐Dimensions
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