A Lower Bound for the Fundamental Frequency of a Convex Region

DOI10.2307/2043987zbMath0476.35060OpenAlexW4230848217MaRDI QIDQ3933360

Murray H. Protter

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/2043987

zbMATH Keywords

convex regionbounded convex regionHersch's resultlower bound for the first eigenvalue of the n-dimensional Laplacian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (18)

On principal frequencies and inradius in convex sets ⋮ A comparison principle for the Lane-Emden equation and applications to geometric estimates ⋮ Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain ⋮ On a class of Cheeger inequalities ⋮ On the remainder term of the Berezin inequality on a convex domain ⋮ Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators ⋮ A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains ⋮ A Brascamp-Lieb-Luttinger–type inequality and applications to symmetric stable processes ⋮ On principal frequencies, volume and inradius in convex sets ⋮ Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals ⋮ On the Cheeger inequality for convex sets ⋮ Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle ⋮ Asymptotic boundary observability for the wave equation on one side of a planar triangle ⋮ Erratum to: ``Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains ⋮ The fractional Makai-Hayman inequality ⋮ Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains ⋮ Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius ⋮ On Blaschke-Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue

Cites Work

• Estimate on the fundamental frequency of a drum
• Lower bounds for the first eigenvalue of elliptic equations
• Sur la frequence fondamentale d'une membrane vibrante: evaluations par defaut et principe de maximum
• A note on Hayman's theorem on the bass note of a drum
• On the mean value of the fundamental mode in the fixed membrane problem
• Some bounds for principal frequency
• Bonnesen-Style Isoperimetric Inequalities

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