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On the first eigenvalue of the clamped plate

https://doi.org/10.1007/bf01762146
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/sapm1952311294openalex-snapshot
Nodal Lines of a Vibrating Plate
inferredcites →https://doi.org/10.1007/bf01203619openalex-snapshot
Beweis des Satzes, da� von allen homogenen Membranen gegebenen Umfanges und gegebener Spannung die kreisf�rmige den tiefsten Grundton besitzt
inferredcites →https://doi.org/10.1007/bf01594119openalex-snapshot
Results of the eigenvalue problem for the plate equation
inferredcites →https://doi.org/10.1007/bf02411942openalex-snapshot
Nonlinear elliptic equations, rearrangements of functions and orlicz spaces
inferredcites →https://doi.org/10.1016/0196-8858(80)90018-4openalex-snapshot
On the structure of biharmonic functions satisfying the clamped plate conditions on a right angle
inferredcites →https://doi.org/10.1073/pnas.44.4.314openalex-snapshot
NOTE TO MY PAPER “ON MEMBRANES AND PLATES”
inferredcites →https://doi.org/10.1090/s0002-9947-1959-0110078-1openalex-snapshot
Curvature Measures
inferredcites →https://doi.org/10.1090/s0025-5718-1972-0312751-9openalex-snapshot
Block Five Diagonal Matrices and the Fast Numerical Solution of the Biharmonic Equation
inferredcites →https://doi.org/10.1137/1009070openalex-snapshot
Isoperimetric Inequalities and Their Applications
inferredcites →https://doi.org/10.1515/9781400882663openalex-snapshot
Isoperimetric Inequalities in Mathematical Physics. (AM-27)

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/cpa.22090openalex-snapshot
A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions
inferred← citeshttps://doi.org/10.1007/978-3-031-53740-0_5openalex-snapshot
The Kernel of the Strain Tensor for Solenoidal Vector Fields with Homogeneous Normal Trace
inferred← citeshttps://doi.org/10.1007/978-3-0348-8942-1_9openalex-snapshot
Inequalities for the first eigenvalues of the clamped plate and buckling problems
inferred← citeshttps://doi.org/10.1007/978-3-319-41538-3_5openalex-snapshot
Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator
inferred← citeshttps://doi.org/10.1007/978-94-011-4577-0_2openalex-snapshot
Open Problems on Eigenvalues of the Laplacian
inferred← citeshttps://doi.org/10.1007/bf00375124openalex-snapshot
Rayleigh's conjecture on the principal frequency of the clamped plate
inferred← citeshttps://doi.org/10.1007/bfb0072690openalex-snapshot
Rearrangements of functions and partial differential equations
inferred← citeshttps://doi.org/10.1007/bfb0086796openalex-snapshot
Some topics in symmetrization
inferred← citeshttps://doi.org/10.1007/bfb0106741openalex-snapshot
Some nonconvex shape optimization problems
inferred← citeshttps://doi.org/10.1007/s000000050100openalex-snapshot
The role of positive boundary data in generalized clamped plate equations
inferred← citeshttps://doi.org/10.1007/s00039-022-00606-7openalex-snapshot
Lord Rayleigh’s Conjecture for Vibrating Clamped Plates in Positively Curved Spaces
inferred← citeshttps://doi.org/10.1007/s00205-024-01972-2openalex-snapshot
Towards the Optimality of the Ball for the Rayleigh Conjecture Concerning the Clamped Plate
inferred← citeshttps://doi.org/10.1007/s00205-025-02082-3openalex-snapshot
Minimality of Vortex Solutions to Ginzburg–Landau Type Systems for Gradient Fields in the Unit Ball in Dimension $$N\ge 4$$
inferred← citeshttps://doi.org/10.1007/s00220-010-1171-zopenalex-snapshot
An Isoperimetric Inequality for Fundamental Tones of Free Plates
inferred← citeshttps://doi.org/10.1007/s00220-025-05439-7openalex-snapshot
Fourth Order Saint-Venant Inequalities: Maximizing Compliance and Mean Deflection Among Clamped Plates
inferred← citeshttps://doi.org/10.1007/s10231-010-0142-5openalex-snapshot
Maximization and minimization in problems involving the bi-Laplacian
inferred← citeshttps://doi.org/10.1007/s10231-014-0447-xopenalex-snapshot
Higher-order functional inequalities related to the clamped 1-biharmonic operator
inferred← citeshttps://doi.org/10.1007/s10231-016-0550-2openalex-snapshot
The clamped plate in Gauss space
inferred← citeshttps://doi.org/10.1007/s10231-024-01454-yopenalex-snapshot
Sufficient conditions yielding the Rayleigh Conjecture for the clamped plate
inferred← citeshttps://doi.org/10.1007/s10915-016-0222-9openalex-snapshot
Minimizing Eigenvalues for Inhomogeneous Rods and Plates
inferred← citeshttps://doi.org/10.1007/s13373-011-0017-0openalex-snapshot
Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
inferred← citeshttps://doi.org/10.1016/0022-0396(88)90015-0openalex-snapshot
Super-solutions of eigenvalue problems and the oscillation properties of second order evolution equations
inferred← citeshttps://doi.org/10.1016/0196-8858(92)90006-iopenalex-snapshot
On the fundamental eigenfunctions of a clamped punctured disk
inferred← citeshttps://doi.org/10.1016/b978-0-444-89597-4.50015-9openalex-snapshot
On Isoperimetric Theorems of Mathematical Physics
inferred← citeshttps://doi.org/10.1016/j.acha.2015.08.001openalex-snapshot
Generalized tight p-frames and spectral bounds for Laplace-like operators
inferred← citeshttps://doi.org/10.1016/j.aim.2011.07.007openalex-snapshot
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
inferred← citeshttps://doi.org/10.1016/j.aim.2020.107113openalex-snapshot
Fundamental tones of clamped plates in nonpositively curved spaces
inferred← citeshttps://doi.org/10.1016/j.jde.2022.11.016openalex-snapshot
An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain
inferred← citeshttps://doi.org/10.1016/j.matpur.2026.103867openalex-snapshot
Extremal problems for clamped plates under tension
inferred← citeshttps://doi.org/10.1016/j.na.2008.11.043openalex-snapshot
Maximization of the first eigenvalue in problems involving the bi-Laplacian
inferred← citeshttps://doi.org/10.1016/j.na.2021.112615openalex-snapshot
Comparison results for solutions to the anisotropic Laplacian with Robin boundary conditions
inferred← citeshttps://doi.org/10.1016/j.na.2025.113864openalex-snapshot
A Talenti comparison result for a class of Neumann boundary value problems
inferred← citeshttps://doi.org/10.1017/cbo9780511566165.007openalex-snapshot
Isoperimetric and universal inequalities for eigenvalues
inferred← citeshttps://doi.org/10.1080/00036811.2010.534727openalex-snapshot
Vibrational modes of circular free plates under tension
inferred← citeshttps://doi.org/10.1080/00036811.2015.1068299openalex-snapshot
An isoperimetric inequality for fundamental tones of free plates with nonzero Poisson’s ratio
inferred← citeshttps://doi.org/10.1080/17476933.2019.1624730openalex-snapshot
Evolution of the first eigenvalue of the clamped plate on manifold along the Ricci flow
inferred← citeshttps://doi.org/10.1090/conm/552/10909openalex-snapshot
Isoperimetric inequalities for eigenvalues of the Laplacian
inferred← citeshttps://doi.org/10.1090/qam/856187openalex-snapshot
Positive deflections of elastic beams
inferred← citeshttps://doi.org/10.1112/plms.70079openalex-snapshot
Principal frequency of clamped plates on RCD(0,N)${\sf RCD}(0,N)$ spaces: Sharpness, rigidity, and stability
inferred← citeshttps://doi.org/10.1215/s0012-7094-95-07801-6openalex-snapshot
On Rayleigh’s conjecture for the clamped plate and its generalization to three dimensions
inferred← citeshttps://doi.org/10.1515/ans-2023-0194openalex-snapshot
Talenti comparison results and rigidity results for anisotropic p-Laplacian operator with Robin boundary conditions
inferred← citeshttps://doi.org/10.3934/cpaa.2020007openalex-snapshot
Estimates for sums of eigenvalues of the free plate via the fourier transform
inferred← citeshttps://doi.org/10.4171/jst/413openalex-snapshot
A sharp isoperimetric inequality for the second eigenvalue of the Robin plate
inferred← citeshttps://doi.org/10.4310/jdg/1659987895openalex-snapshot
Bounded multiplicity for eigenvalues of a circular vibrating clamped plate
inferred← citeshttps://doi.org/10.5565/publmat6812412openalex-snapshot
Oscillatory phenomena for higher-order fractional Laplacians
inferred← citeshttps://doi.org/10.7153/dea-01-12openalex-snapshot
Optimization of the first eigenvalue in problems involving the bi-Laplacian
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