Sharp bounds for eigenvalues of triangles

DOI10.1307/mmj/1187646992zbMath1148.35056arXivmath/0603630OpenAlexW1991732914MaRDI QIDQ2469304

Bartłomiej A. Siudeja

Publication date: 5 February 2008

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

Full work available at URL: https://arxiv.org/abs/math/0603630

zbMATH Keywords

eigenvaluesmembrane problemtriangles

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Membranes (74K15) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

Related Items (10)

A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains ⋮ Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian ⋮ Sums of Laplace eigenvalues-rotationally symmetric maximizers in the plane ⋮ Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals ⋮ Maximizing Neumann fundamental tones of triangles ⋮ Minimizing Neumann fundamental tones of triangles: an optimal Poincaré inequality ⋮ On the Cheeger inequality for convex sets ⋮ On the inverse spectral problem for Euclidean triangles ⋮ Efficiency and localisation for the first Dirichlet eigenfunction ⋮ A proof of the triangular Ashbaugh-Benguria-Payne-Pólya-Weinberger inequality

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• A note on Hayman's theorem on the bass note of a drum
• Upper and lower bounds for the first Dirichlet eigenvalue of a triangle
• New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions
• The Eigenvalues of an Equilateral Triangle
• “Best possible” upper and lower bounds for the zeros of the Bessel function 𝐽_{𝜈}(𝑥)
• Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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