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Eigenfunction concentration for polygonal billiards

Hassell, Andrew; Hillairet, Luc; Marzuola, Jeremy

Description

In this note, we extend the results on eigenfunction concentration in billiards as proved by the third author in [8]. There, the methods developed in Burq and Zworski [3] 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 neighborhood U of the vertices, there is a lower bound, for some c=c(U)>0 and any...[Show more]

CollectionsANU Research Publications
Date published: 2009
Type: Journal article
URI: http://hdl.handle.net/1885/37098
Source: Communications in Partial Differential Equations
DOI: 10.1080/03605300902768909

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