Nonconcentration in partially rectangular billiards

Details Nonconcentration in partially rectangular billiards Nonconcentration in partially rectangular billiards

2010-11-25

arxiv.org/abs/1011.5562v2

Mathematics

Analysis of PDEs

28 pages, 1 figure; Typos corrected, error in final proof corrected and techniques strengthened

Scientific paper

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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