TY - JOUR
T1 - Eigenfunction concentration for polygonal billiards
AU - Hassell, Andrew
AU - Hillairet, Luc
AU - Marzuola, Jeremy
PY - 2009/5
Y1 - 2009/5
N2 - 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 eigenfunction u.
AB - 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 eigenfunction u.
KW - Control region
KW - Eigenfunction concentration
KW - Polygonal billiards
KW - Semiclassical measures
UR - http://www.scopus.com/inward/record.url?scp=68949202231&partnerID=8YFLogxK
U2 - 10.1080/03605300902768909
DO - 10.1080/03605300902768909
M3 - Article
SN - 0360-5302
VL - 34
SP - 475
EP - 485
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 5
ER -