Minimizing Neumann fundamental tones of triangles: An optimal Poincaré inequality

R. S. Laugesen; B. A. Siudeja

doi:10.1016/j.jde.2010.02.020

Minimizing Neumann fundamental tones of triangles: An optimal Poincaré inequality

R. S. Laugesen, B. A. Siudeja

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The first nonzero eigenvalue of the Neumann Laplacian is shown to be minimal for the degenerate acute isosceles triangle, among all triangles of given diameter. Hence an optimal Poincaré inequality for triangles is derived.The proof relies on symmetry of the Neumann fundamental mode for isosceles triangles with aperture less than π/3. Antisymmetry is proved for apertures greater than π/3 copy; 2010 Elsevier Inc.

Original language	English (US)
Pages (from-to)	118-135
Number of pages	18
Journal	Journal of Differential Equations
Volume	249
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2010.02.020
State	Published - Jul 2010

Keywords

Free membrane
Isodiametric
Isoperimetric
Poincaré inequality

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jde.2010.02.020

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abstract = "The first nonzero eigenvalue of the Neumann Laplacian is shown to be minimal for the degenerate acute isosceles triangle, among all triangles of given diameter. Hence an optimal Poincar{\'e} inequality for triangles is derived.The proof relies on symmetry of the Neumann fundamental mode for isosceles triangles with aperture less than π/3. Antisymmetry is proved for apertures greater than π/3 copy; 2010 Elsevier Inc.",

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AU - Siudeja, B. A.

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AB - The first nonzero eigenvalue of the Neumann Laplacian is shown to be minimal for the degenerate acute isosceles triangle, among all triangles of given diameter. Hence an optimal Poincaré inequality for triangles is derived.The proof relies on symmetry of the Neumann fundamental mode for isosceles triangles with aperture less than π/3. Antisymmetry is proved for apertures greater than π/3 copy; 2010 Elsevier Inc.

KW - Free membrane

KW - Isodiametric

KW - Isoperimetric

KW - Poincaré inequality

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Minimizing Neumann fundamental tones of triangles: An optimal Poincaré inequality

Abstract

Keywords

ASJC Scopus subject areas

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