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Extensions of an
inequality by Pólya and Schiffer for vibrating membranes
Catherine Bandle |
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Vol. 42 (1972), No. 3, 543–555
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Abstract |
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The inequality by Pólya and Schiffer considered in this paper is concerned with the sume of the n first reciprocal eigenvalues of the problem Δu + λu = 0 in G,u = 0 on ∂G. First we extend this inequality to the problem of an inhomogeneous membrane Δu + λρu = 0 in G,u = 0 on ∂G. Then we prove a sharper form of it for a class of homogeneous membranes with partially free boundary. The proofs are based on a variational characterization for the eigenvalues and use conformal mapping and transplantation arguments. |
Mathematical Subject Classification 2000
Primary: 49G05
Secondary: 52A40, 53A99, 49F10
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Milestones
Received: 8 June 1971
Published: 1 September 1972
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Authors |
| Catherine Bandle | |
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