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An isoperimetric inequality for the first eigenfunction in the fixed membrane problem. (English) Zbl 0241.73080


MSC:

74K15 Membranes
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References:

[1] P. Garabedian,Partial Differential Equations (John Wiley, New York 1964). · Zbl 0124.30501
[2] L.E. Payne,Isoperimetric Inequalities and their Applications, SIAM Review9, 453 (1967). · Zbl 0154.12602
[3] G. Pólya andG. Szegö,Isoperimetric Inequalities in Mathematical Physics, Ann. Math. Studies27 (Princeton University Press, Princeton 1951).
[4] R.P. Sperb,Obere und untere Schranken für den tiefsten Eigenwert bzw. das Energieintegral in Problemen, die einen Parameter {\(\alpha\)} enthalten, Diss. ETH, Juris Druck+Verlag Zürich, 1971.
[5] R.P. Sperb,Untere und obere Schranken für den tiefsten Eigenwert der elastisch gestützten Membran, to appear in Z. angew. Math. Phys. · Zbl 0246.73072
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