A sharp isoperimetric inequality for the second eigenvalue of the Robin plate

DOI10.4171/JST/413zbMath1498.35369arXiv2010.10576MaRDI QIDQ2080323

Jeffrey J. Langford, Laura Mercredi Chasman

Publication date: 7 October 2022

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.10576

zbMATH Keywords

isoperimetric inequalityRobin boundary conditionsBessel functionbi-Laplacian

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Plates (74K20) Estimates of eigenvalues in context of PDEs (35P15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items

PDE comparison principles for Robin problems, An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An isoperimetric inequality for fundamental tones of free plates
• The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization
• A variational approach to the isoperimetric inequality for the Robin eigenvalue problem
• Partial differential equations. I: Basic theory
• On the first eigenvalue of a fourth order Steklov problem
• On the first eigenvalue of the clamped plate
• On the stability of some isoperimetric inequalities for the fundamental tones of free plates
• Rayleigh's conjecture on the principal frequency of the clamped plate
• On Rayleigh's conjecture for the clamped plate and its generalization to three dimensions
• A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter
• The first Robin eigenvalue with negative boundary parameter
• On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue
• Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
• A Faber-Krahn inequality for Robin problems in any space dimension
• On the Eigenvalues of a Biharmonic Steklov Problem
• An isoperimetric inequality for fundamental tones of free plates with nonzero Poisson’s ratio
• Vibrational modes of circular free plates under tension
• Remarks on strongly elliptic partial differential equations
• From Steklov to Neumann and Beyond, via Robin: The Szegő Way
• On an Isoperimetric Inequality for the First Eigenvalue of a Boundary Value Problem
• Bounds and Monotonicities for the Zeros of Derivatives of Ultraspherical Bessel Functions
• From Neumann to Steklov and beyond, via Robin: The Weinberger way
• The Bilaplacian with Robin Boundary Conditions
• Robin spectrum: two disks maximize the third eigenvalue