Journal d’Analyse Mathématique

, Volume 95, Issue 1, pp 323–332 | Cite as

Sums of free membrane eigenvalues



LetD be a simply connected domain in the plane which is the image of the unit disk under a normalized conformal mapping, and let μ1=0<μ2≤μ3 be the free membrane eigenvalues. We prove that for anyn≥2,
$$A\sum\limits_2^n {\frac{1}{{\mu _j }} \geqslant \pi } \sum\limits_2^n {\frac{1}{{\mu _j ^{(o)} }}} $$
whereA is the area of the domainD and μ j (o) are the free membrane eigenvalues of the unit disk.


Unit Disk Connected Domain Isoperimetric Inequality Variational Characterization Neumann Function 


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Copyright information

©  0251 V 2 2005

Authors and Affiliations

  1. 1.Fachbereich Mathematik und Informatik Institut für AnalysisMartin-Luther-Universität Halle-WittenbergHalleGermany

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