Eigenfunction concentration for polygonal billiards

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dc.creatorHassell, Andrew
dc.creatorHillairet, Luc
dc.creatorMarzuola, Jeremy
dc.date2008-05-26
dc.date2008-09-29
dc.date.accessioned2026-07-07T10:05:35Z
dc.date.available2026-07-07T10:05:35Z
dc.descriptionIn this note, we extend the results on eigenfunction concentration in billiards as proved by the third author in \cite{M1}. There, the methods developed in Burq-Zworski \cite{BZ3} to study eigenfunctions for billiards which have rectangular components were applied. Here we take an arbitrary polygonal billiard $B$ and show that eigenfunction mass cannot concentrate away from the vertices; in other words, given any neighbourhood $U$ of the vertices, there is a lower bound $$ \int_U |u|^2 \geq c \int_B |u|^2 $$ for some $c = c(U) > 0$ and any eigenfunction $u$.
dc.description9 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0805.3826
dc.identifierhttp://arxiv.org/abs/0805.3826
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170049
dc.subjectAnalysis of PDEs
dc.subject35Q40
dc.titleEigenfunction concentration for polygonal billiards
dc.typetext

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