On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions

Let Ω be open bounded set of IRn, whose boundary us of cluss C2 and let Ω(∞) be thcx set of whzch lic at a dtstance less than ∊ of Ω. CVt show that the p-th czqenvalue converges to the p-th eigenvalue λ of the Laplace-Beltrami oprator on δω. Ifλp Ap as sztnple, we give limit of . as ∊ tends to 0. These results are written zn thc language of analysis , and no knowledge of differntial geometry assumed.