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Free membrane eigenvalues

Authors:

Bodo Dittmar

Institution:

1. Martin-Luther Universit?t Halle-Wittenberg, Institut für Mathematik, Hoher Weg 4, 06099, Halle, Saale, Germany

Abstract:

For a simply connected and normalized domain D in the plane it was proven by Pólya and Schiffer in 1954 for the fixed membrane eigenvalues

$\sum \limits^{n}_{1} \frac{1}{{\lambda}_j} \geq \sum \limits^{n}_{1} \frac{1}{{\lambda}^{(0)}_j}$

for any n, where λ_j⁽⁰⁾ are the fixed membrane eigenvalues of the unit disk. The purpose of this paper is to prove an analog inequality for the free membrane eigenvalues.

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35P15

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