Spectral inequalities of the Laplacian on a curved tube with varying cross section
Commun. Korean Math. Soc. 2013 Vol. 28, No. 1, 177-181
https://doi.org/10.4134/CKMS.2013.28.1.177
Printed January 31, 2013
Jing Mao and Lanbao Hou
Technical University of Lisbon, JingChu University of Technology
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 \cite{ppd}.
Keywords : spectral threshold, curved tubes, cross section, Bessel function
MSC numbers : 35P15, 58C40
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