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SPECTRAL INEQUALITIES OF THE LAPLACIAN ON A CURVED TUBE WITH VARYING CROSS SECTION

Mao, Jing;Hou, Lanbao

  • 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].

Keywords

spectral threshold;curved tubes;cross section;Bessel function

References

  1. 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