Inequalities for the minimal eigenvalue of the Laplacian in an annulus

Details Inequalities for the minimal eigenvalue of the Laplacian in an annulus Inequalities for the minimal eigenvalue of the Laplacian in an annulus

1999-11-27

arxiv.org/abs/math-ph/9911040v1

Math. Inequalitie and Applications, 1, N4, (1998), 559-563

Physics

Mathematical Physics

Scientific paper

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.

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