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.
- [1] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- [2] E. B. Davies and B. Simon, Spectral properties of Neumann Laplacian of horns, Geom. Funct. Anal. 2 (1992), no. 1, 105–117. MR 1143665, https://doi.org/10.1007/BF01895707
- [3] 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, https://doi.org/10.1016/0022-1236(91)90130-W
- [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
