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arXiv · 1305.4653

A non-concentration estimate for partially rectangular billiards

Hans Christianson
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Abstract

We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any $ε_0>0$, an $Ø(λ^{-ε_0})$ quasimode must have $L^2$ mass in the "wings" bounded below by $λ^{-2-δ}$ for any $δ>0$. The proof uses the author's recent work on 0-Gevrey smooth domains to approximate quasimodes on $C^{1,1}$ domains. There is an improvement for $C^{2,α}$ domains.

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Hans Christianson. 2013-09-13. A non-concentration estimate for partially rectangular billiards. https://arxiv.org/abs/1305.4653

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