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Nonconcentration in
partially rectangular billiards
Luc Hillairet and Jeremy L. Marzuola |
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Vol. 5 (2012), No. 4, 831–854
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Abstract |
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In specific types of partially rectangular billiards we estimate the mass of an eigenfunction of energy 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 is not resonating with the Dirichlet spectrum of the rectangular part. |
Keywords
eigenfunctions, billiards, nonconcentration
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Mathematical Subject Classification 2010
Primary: 35P20
Secondary: 35Q40, 58J51
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Milestones
Received: 30 November 2010
Revised: 14 July 2011
Accepted: 24 October 2011
Published: 27 November 2012
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Authors |
| Luc Hillairet | |
| Laboratoire de Mathématiques Jean
Leray UMR 6629 CNRS-Université de Nantes 2 rue de la Houssinière BP 92208 F-44 322 Nantes cedex 3 France |
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| Jeremy L. Marzuola | |
| Mathematics Department University of North Carolina, Chapel Hill Phillips Hall Chapel Hill, NC 27599 United States |
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