Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 16 (2009), No. 3, Page 269-414
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).