Eigenfunction concentration for polygonal billiards

Details Eigenfunction concentration for polygonal billiards Eigenfunction concentration for polygonal billiards

2008-05-26

arxiv.org/abs/0805.3826v2

Mathematics

Analysis of PDEs

9 pages, 3 figures

Scientific paper

In 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 $u$.

Affiliated with

Also associated with

No associations

Rating

Eigenfunction concentration for polygonal billiards does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Eigenfunction concentration for polygonal billiards, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Eigenfunction concentration for polygonal billiards will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-320688