Maximizing Neumann fundamental tones of triangles

R. S. Laugesen; B. A. Siudeja

doi:10.1063/1.3246834

Maximizing Neumann fundamental tones of triangles

R. S. Laugesen, B. A. Siudeja

Mathematics

Research output: Contribution to journal › Article

Abstract

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proven for the harmonic and arithmetic means of the first two nonzero eigenvalues.

Original language	English (US)
Article number	112903
Journal	Journal of Mathematical Physics
Volume	50
Issue number	11
DOIs	https://doi.org/10.1063/1.3246834
State	Published - Dec 24 2009

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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Laugesen, R. S., & Siudeja, B. A. (2009). Maximizing Neumann fundamental tones of triangles. Journal of Mathematical Physics, 50(11), [112903]. https://doi.org/10.1063/1.3246834

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