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Examples of embedded eigenvalues for the Dirichlet Laplacian in perturbed waveguides
Author(s) -
Witsch K. J.
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670120107
Subject(s) - mathematics , eigenvalues and eigenvectors , dirichlet eigenvalue , dirichlet distribution , laplace operator , spectrum (functional analysis) , ball (mathematics) , mathematical analysis , pure mathematics , dirichlet's principle , physics , quantum mechanics , boundary value problem
It is shown that there exist domains Ω ⊂ ℝ N , which outside of some ball coincide with the strip ℝ N − 1 × (0, π) and for which the Dirichlet Laplacian – Δ has eigenvalues within the subinterval (1, 4) of the essential spectrum (1, ∞).