Inequalities for the minimal eigenvalue of the Laplacian in an annulus

1999/11/27 by A. G. Ramm, P. N. Shivakumar
Physics and Astronomy · Mathematics · #math-ph #math.AP #math.MP #msc:35J05 #msc:35P15

paper · pdf

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

arxiv created 1999/11/27 · arxiv updated 2009/11/30

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.

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