2013/05/20 by Hans Christianson, Christianson, Hans
Mathematics · #35P20 #58J51 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P20 #msc:58J51
paper · pdf · doi:10.48550/arxiv.1305.4653
Contains a summary of results from the author's previous work in arXiv:1303.6172 [math.AP]. Version 2 corrects a mistake in notation and add an improved result for $C^{2, α}$ domains. L. Hillairet pointed out a mistake in v.2; v.3 is expanded and corrects this mistake
arxiv created 2013/09/13 · arxiv updated 2013/09/17
We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε0>0, an Ø(λ-ε0) quasimode must have L2 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 C1,1 domains. There is an improvement for C2,α domains.