scientific article; zbMATH DE number 1021780

zbMath0891.73028MaRDI QIDQ4339617

Mark S. Ashbaugh, Richard Snyder Laugesen

Publication date: 24 August 1997

Full work available at URL: http://www.numdam.org/item?id=ASNSP_1996_4_23_2_383_0

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

lower boundsmembranecritical buckling load

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20) Bifurcation and buckling (74G60)

Related Items (25)

Spectral theory for perturbed Krein Laplacians in nonsmooth domains ⋮ On Rayleigh's conjecture for the clamped plate and its generalization to three dimensions ⋮ Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator ⋮ Lower bounds for sums of eigenvalues of the buckling problem ⋮ The clamped plate in Gauss space ⋮ Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume ⋮ Lord Rayleigh's conjecture for vibrating clamped plates in positively curved spaces ⋮ Bounded multiplicity for eigenvalues of a circular vibrating clamped plate ⋮ Fundamental tones of clamped plates in nonpositively curved spaces ⋮ Rellich type identities for eigenvalue problems and application to the Pompeiu problem ⋮ Eigenvalue bounds for the poly-harmonic operators ⋮ Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds ⋮ The eigenvalue problem for the \(\infty \)-Bilaplacian ⋮ Towards the optimality of the ball for the Rayleigh conjecture concerning the clamped plate ⋮ Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem ⋮ Sharper estimates on the eigenvalues of Dirichlet fractional Laplacian ⋮ Generalized tight \(p\)-frames and spectral bounds for Laplace-like operators ⋮ A boundary integral equation approach to computing eigenvalues of the Stokes operator ⋮ An isoperimetric inequality for fundamental tones of free plates ⋮ A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains ⋮ Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles ⋮ Estimates for the first eigenvalues of bi-drifted Laplacian on smooth metric measure space ⋮ A sharp isoperimetric inequality for the second eigenvalue of the Robin plate ⋮ Refined eigenvalue bounds on the Dirichlet fractional Laplacian ⋮ Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds

Cites Work

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• Contractive zero-divisors in Bergman spaces
• Rearrangements and convexity of level sets in PDE
• On the first eigenvalue of the clamped plate
• On the fundamental eigenfunctions of a clamped punctured disk
• Methods of intermediate problems for eigenvalues. Theory and ramifications
• Über die Rayleighsche Vermutung: Unter allen Platten von gegebener Fläche und konstanter Dichte und Elastizität hat die kreisförmige den tiefsten Grundton
• Lower bounds to fundamental frequencies and buckling loads of columns and plates
• On Rayleigh's conjecture for the clamped plate and its generalization to three dimensions
• Extremal eigenvalue problems for starlike planar domains
• Monotonicity of the zeros of a cross product of Bessel functions
• Bounding eigenvalues of clamped plates
• Upper and lower bounds for eigenvalues by finite differences
• Untere Schranken für die Eigenwerte positiv-definiter, selbstadjungierter Operatoren
• On Green's function for the biharmonic equation in a right angle wedge
• On the characteristic frequencies of a symmetric membrane
• Elliptical Membranes with Smallest Second Eigenvalue
• NOTE TO MY PAPER “ON MEMBRANES AND PLATES”
• ON SIGN VARIATION AND THE ABSENCE OF "STRONG" ZEROS OF SOLUTIONS OF ELLIPTIC EQUATIONS
• Upper and lower bounds for frequencies of clamped rhombical plates
• On the Structure of Solutions $\Delta ^2 u = \lambda u$ Which Satisfy the Clamped Plate Conditions on a Right Angle
• More Bounds on Eigenvalue Ratios for Dirichlet Laplacians inNDimensions
• Approximations and Bounds for Eigenvalues of Elliptic Operators
• Computational Methods for Determining Lower Bounds for Eigenvalues of Operators in Hilbert Spaces
• Upper and Lower Bounds for the Frequencies of Rectangular Cantilever Plates
• Pointwise Bounds in the First Biharmonic Boundary Value Problem
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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