On the spectrum of the Dirichlet Laplacian for horn-shaped regions in Rn with infinite volume

Examples of embedded eigenvalues for the

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

✍ Karl J. Witsch 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 272 KB

## 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