Concentration and confinement of eigenfunctions in a bounded open set (version 2)

Assia Benabdallah, Matania Ben-Artzi, Yves Dermenjian

Consider the Dirichlet-Laplacian in $\Omega :=(0,L)\times (0,H)$ and choose another open set $\omega \subset \Omega$. The estimate $0<C_ω\leq R_ω(u):=\frac{\Vert u\Vert^{2}_{L^{2}(ω)}}{\Vert u\Ver…