References
- P. Exner, P. Freitas, and D. Krejcirlk, A lower bound to the spectral threshold in curved tubes, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004), no. 2052, 3457-3467. https://doi.org/10.1098/rspa.2004.1356
Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 28 Issue 1
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- Pages.177-181
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- 2013
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
DOI QR Code
SPECTRAL INEQUALITIES OF THE LAPLACIAN ON A CURVED TUBE WITH VARYING CROSS SECTION
- Mao, Jing (Departamento de Matematica Instituto Superior Tecnico Technical University of Lisbon) ;
- Hou, Lanbao (School of Mathematics and Physics JingChu University of Technology)
- Received : 2012.01.24
- Published : 2013.01.31
Abstract
In this note, we consider a curved tube with varying cross-section formed by rotating open bounded Euclidean domains with respect to a reference curve, and successfully give a lower bound to the threshold of the Laplacian on the tube, subject to Dirichlet boundary conditions on the surface and Neumann conditions at the ends of the tube. This generalizes the corresponding result in [1].