A Non-Concentration Estimate for Partially Rectangular Billiards

We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε₀ > 0, an 𝒪(λ^?ε₀ ) quasimode must have L ² mass in the “wings” (in phase space) 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 ^{k, α} and C ^∞ domains.