Abstract
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.
Citation
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
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