%0 Journal Article
%T Nonconcentration in partially rectangular billiards
%A Luc Hillairet
%A Jeremy L. Marzuola
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1011.5562v2