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Article Dans Une Revue Communications in Partial Differential Equations Année : 2009

Eigenfunction concentration for polygonal billiards

Luc Hillairet
Jeremy L. Marzuola
  • Fonction : Auteur

Résumé

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 $u$.

Dates et versions

hal-00345660 , version 1 (09-12-2008)

Identifiants

Citer

Andrew Hassell, Luc Hillairet, Jeremy L. Marzuola. Eigenfunction concentration for polygonal billiards. Communications in Partial Differential Equations, 2009, 34 (4-6), pp.475--485. ⟨hal-00345660⟩
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