Inequalities for the minimal eigenvalue of the Laplacian in an annulus
Mathematical Physics
2007-05-23 v1 Analysis of PDEs
math.MP
Abstract
It is proved that the minimal Dirichlet eigenvalue of the Laplacian in an annulus is a monotonically decreasing function of the displacement of the center of the smaller disc. The maximal value of the minimal eigenvalue is attained when the annulus is formed by two concentric discs.
Cite
@article{arxiv.math-ph/9911040,
title = {Inequalities for the minimal eigenvalue of the Laplacian in an annulus},
author = {A. G. Ramm and P. N. Shivakumar},
journal= {arXiv preprint arXiv:math-ph/9911040},
year = {2007}
}