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 | References | Similar Articles | Additional Information
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.
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- E. B. Davies and B. Simon, Spectral properties of Neumann Laplacian of horns, Geom. Funct. Anal. 2 (1992), no. 1, 105–117. MR 1143665, DOI https://doi.org/10.1007/BF01895707
- Rainer Hempel, Luis A. Seco, and Barry Simon, The essential spectrum of Neumann Laplacians on some bounded singular domains, J. Funct. Anal. 102 (1991), no. 2, 448–483. MR 1140635, DOI https://doi.org/10.1016/0022-1236%2891%2990130-W 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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Article copyright:
© Copyright 1992
American Mathematical Society
