The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends

Details The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends

2009-10-08

arxiv.org/abs/0910.1454v1

Siam Journal on Mathematical Analysis, vol. 42 (2010), p. 2581-2609

Mathematics

Spectral Theory

25 pages, 10 figures

Scientific paper

10.1137/090755680

A simple sufficient condition on curved end of a straight cylinder is found that provides a localization of the principal eigenfunction of the mixed boundary value for the Laplace operator with the Dirichlet conditions on the lateral side. Namely, the eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior. Similar effects are observed in the Dirichlet and Neumann problems, too.

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