Two new Weyl-type bounds for the Dirichlet Laplacian

DOI10.1090/S0002-9947-07-04254-7zbMath1132.35065arXiv0711.4067MaRDI QIDQ5437604

Lotfi Hermi

Publication date: 21 January 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4067

zbMATH Keywords

Dirichlet problemWeyl asymptoticsNeumann problemeigenvalues of the LaplacianKröger boundsLi-Yau bounds

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items

BOUNDS FOR THE EIGENVALUES OF THE FRACTIONAL LAPLACIAN ⋮ Upper bound estimates of eigenvalues for Hörmander operators on non-equiregular sub-Riemannian manifolds ⋮ Estimates of Dirichlet eigenvalues for degenerate \(\triangle_\mu\)-Laplace operator ⋮ Eigenvalue estimates for magnetic Schrödinger operators in domains ⋮ Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues ⋮ Estimates on the eigenvalues of the clamped plate problem on domains in Euclidean spaces ⋮ On Riesz Means of Eigenvalues ⋮ Estimates the upper bounds of Dirichlet eigenvalues for fractional Laplacian ⋮ Trace identities for commutators, with applications to the distribution of eigenvalues

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Schrödinger equation and the eigenvalue problem
• Lower bounds for the eigenvalues of the fixed vibrating membrane problems
• On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics
• Isoperimetric bound for \(\lambda{}_ 3 /\lambda{}_ 2\) for the membrane problem
• Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space
• Some inequalities between Dirichlet and Neumann eigenvalues
• A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions
• Dirichlet and Neumann eigenvalue problems on domains 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
• On the Ratio of Consecutive Eigenvalues
• Can One Hear the Shape of a Drum? Revisited
• Eigenvalues of the Laplacian on inhomogeneous membranes
• On the Eigenvalues of Vibrating Membranes^†
• Proof of the Payne-Pólya-Weinberger conjecture
• More Bounds on Eigenvalue Ratios for Dirichlet Laplacians inNDimensions
• Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem
• Bounds for Ratios of Eigenvalues of the Dirichlet Laplacian
• Universal Bounds for the Low Eigenvalues of Neumann Laplacians inNDimensions
• Can One Hear the Shape of a Drum?
• On a Theorem of Polya
• On the Ratio of Consecutive Eigenvalues in N‐Dimensions
• Fourier Tauberian theorems and applications