Concentration and confinement of eigenfunctions in a bounded open set (version 2)
Assia Benabdallah, Matania Ben‐Artzi, Yves Dermenjian · arXiv (Cornell University) · 2019
Consider the Dirichlet-Laplacian in $Ω:= (0,L)\times (0,H)$ and choose another open set $ω\subset Ω$. The estimate $0C_ω>0,\exists ω, ω ot=\emptyset$, such that $\inf R_ω(u)=0$,and we wish to characterize these two sets. For two patterns we give a sufficient condition, sometimes necessary. As our operator corresponds to a layered media we can give another representation of its spectrum: i.e. a subset of points of $R\times R$ that leads to the suggested partition and others connected results: micro local interpretation, default measures,... Section 4.1 of the previous version was not correct, now it is corrected, many proofs are simplified and a new general result is added.