On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions
- 1 August 1996
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 61 (3-4) , 293-306
- https://doi.org/10.1080/00036819608840461
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- Elliptic Partial Differential Equations of Second OrderPublished by Springer Nature ,1977