Isoperimetric bound for \(\lambda{}_ 3 /\lambda{}_ 2\) for the membrane problem

DOI10.1215/S0012-7094-91-06313-1zbMath0747.35023OpenAlexW2036481334WikidataQ59158317 ScholiaQ59158317MaRDI QIDQ1179167

Mark S. Ashbaugh, Rafael D. Benguria

Publication date: 26 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06313-1

zbMATH Keywords

Rayleigh-Ritz minimum problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian, Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem, Bounds for ratios of the membrane eigenvalues, Bounds for Ratios of Eigenvalues of the Dirichlet Laplacian, Two new Weyl-type bounds for the Dirichlet Laplacian

Cites Work

• Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials
• A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions
• On the characteristic frequencies of a symmetric membrane
• On the Ratio of Consecutive Eigenvalues
• Some unsolved problems in the theory of differential equations and mathematical physics
• Proof of the Payne-Pólya-Weinberger conjecture
• On the Ratio of Consecutive Eigenvalues in N‐Dimensions
• Unnamed Item
• Unnamed Item