Resonance widths for general Helmholtz resonators with straight neck

Thomas Duyckaerts; Alain Grigis; André Martinez

doi:10.1215/00127094-3644795

Abstract

We prove an optimal exponential lower bound on the width of the resonance associated to the first eigenvalue of the cavity for a general Helmholtz resonator with straight neck, in any dimension.

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Thomas Duyckaerts. Alain Grigis. André Martinez. "Resonance widths for general Helmholtz resonators with straight neck." Duke Math. J. 165 (14) 2793 - 2810, 1 October 2016. https://doi.org/10.1215/00127094-3644795

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Received: 5 May 2015; Revised: 9 September 2015; Published: 1 October 2016

First available in Project Euclid: 20 July 2016

zbMATH: 1366.81167

MathSciNet: MR3551774

Digital Object Identifier: 10.1215/00127094-3644795

Subjects:

Primary: 81Q20

Secondary: 35B34 , 35P15

Keywords: Helmholtz resonator , lower bound , scattering resonances

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