Eigenvalue Asymptotics of Narrow Domains

Lanbo Fang

In this paper, we considered the spectrum of the Dirichlet Laplacian ${\Delta }_{\epsilon }$ on ${\Omega }_{\epsilon }=\{(x,y):-l_1<x<l_2,0<y<\epsilon h(x)]\}$ where $l_1,l_2>0$ and $h(x)$ is a positive analytic function…