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2012 Nonconcentration in partially rectangular billiards
Luc Hillairet, Jeremy Marzuola
Anal. PDE 5(4): 831-854 (2012). DOI: 10.2140/apde.2012.5.831

Abstract

In specific types of partially rectangular billiards we estimate the mass of an eigenfunction of energy E in the region outside the rectangular set in the high-energy limit. We use the adiabatic ansatz to compare the Dirichlet energy form with a second quadratic form for which separation of variables applies. This allows us to use sharp one-dimensional control estimates and to derive the bound assuming that E is not resonating with the Dirichlet spectrum of the rectangular part.

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Luc Hillairet. Jeremy Marzuola. "Nonconcentration in partially rectangular billiards." Anal. PDE 5 (4) 831 - 854, 2012. https://doi.org/10.2140/apde.2012.5.831

Information

Received: 30 November 2010; Revised: 14 July 2011; Accepted: 24 October 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1264.35155
MathSciNet: MR3006643
Digital Object Identifier: 10.2140/apde.2012.5.831

Subjects:
Primary: 35P20
Secondary: 35Q40, 58J51

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.5 • No. 4 • 2012
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