Examples of embedded eigenvalues for the Dirichlet‐Laplacian in domains with infinite boundaries
Karl J. Witsch · Mathematical Methods in the Applied Sciences · 1990
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.