An Asymptotic Formula Concerning the Eigenvalues of the Dirichlet Laplacian in a Planar Domain
✍ Scribed by DostaniÄ, M. R.
- Book ID
- 120569399
- Publisher
- Springer Netherlands
- Year
- 2013
- Tongue
- English
- Weight
- 266 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0926-2601
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📜 SIMILAR VOLUMES
## Abstract For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross‐section whose diameter
## Abstract We study the asymptotic behavior of the eigenelements of the Dirichlet problem for the Laplacian in a two‐dimensional bounded domain with thin shoots, depending on a small parameter ε. Under the assumption that the width of the shoots goes to zero, as ε tends to zero, we construct the l