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Examples of embedded eigenvalues for the Dirichlet-Laplacian in domains with infinite boundaries

✍ Scribed by Karl J. Witsch

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 272 KB
Volume: 12
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670120208

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✦ Synopsis

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 in some bounded subset is greater than at infinity.

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