Eigenvalue Asymptotics of Narrow Domains

Abstract

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 having $0$ the only point where it achieves its global maximum $M$. In particular we studied in details about the full asymptotics of the eigenvalues.

References in corpus (2)

• Convergence of spectra of graph-like thin manifolds
• Twisting versus bending in quantum waveguides