An asymptotic formula for the eigenvalues of the Laplacian in a domain with a small hole
Shin Ozawa · Proceedings of the Japan Academy Series A Mathematical Sciences · 1982
This note is a continuation of our previous paper [1].Let/2 be a bounded domain in R with C boundary , and w be a fixed point in/2.For any sufficiently small e0, let B, be the ball defined by B,={z e 2;Iz--wle}.Let/2, be the bounded domain defined by/2,-/2 \B,.Then 2, .3B,.Let 0) p()_ p.(e)_.be the eigenvalues of the Laplacian in/2, under the Dirichlet condition on 39,.Let 0/,_Z._.be the eigen- values of the Laplacian in/2 under the Dirichlet condition on r.We