The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends
Spectral Theory
2012-01-11 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0910.1454,
title = {The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends},
author = {G. Cardone and T. Durante and S. A. Nazarov},
journal= {arXiv preprint arXiv:0910.1454},
year = {2012}
}
Comments
25 pages, 10 figures