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The Neumann Laplacian of a jelly roll


Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 114 (1992), 783-785
MSC: Primary 58G25; Secondary 35J05, 35P05
DOI: https://doi.org/10.1090/S0002-9939-1992-1076578-X
MathSciNet review: 1076578
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Abstract: We consider the Laplacian with Neumann boundary conditions of a bounded connected region obtained by removing a suitable infinite spiral from an annulus. We show that the spectrum has an absolutely continuous component.


References [Enhancements On Off] (What's this?)

  • [1] R. Courant and D. Hilbert, Methods of mathematical physics, Interscience, New York, 1953. MR 0065391 (16:426a)
  • [2] E. B. Davies and B. Simon, Spectral properties of the Neumann Laplacian of horns, preprint. MR 1143665 (93g:35099)
  • [3] R. Hempel, L. A. Seco, and B. Simon, The essential spectrum of Neumann Laplacians on some bounded singular domains, preprint. MR 1140635 (93h:35144)
  • [4] V. Jaksic, S. Molchhonov, and B. Simon, Eigenvalue asymptotics of the Neumann Laplacian of the manifolds and regions with cusps, in preparation.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1076578-X
Article copyright: © Copyright 1992 American Mathematical Society

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