Nonconcentration in partially rectangular billiards
Hillairet, Luc · Marzuola, Jeremy L.
Original · EN
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.
English translation
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