Spectra of domains with partial degeneration
Shuichi Jimbo, Satoshi Kosugi · Institutional Repositories DataBase (IRDB) · 2009
We consider the eigenvalue problem of the Laplacian (Neumann B.C.) in the domain which has a very thin subregion. We give an elaborate characterization of the asymptotics of theeigenvalues and the eigenfunctions.The perturbation formulas take various forms depending on the type ofthe eigenvalue and geometric situations (dimension, shape).