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Untere und obere Schranken für den tiefsten Eigenwert der elastisch gestützten Membran. (German) Zbl 0246.73072

74K15 Membranes
35P15 Estimates of eigenvalues in context of PDEs
Full Text: DOI
[1] L.E. Payne undM.E. Rayner,An Isoperimetric Inequality for the First Eigenfunction in the Fixed Membrane Problem, Z. angew. Math. Phys.23, 13–15 (1972). · Zbl 0241.73080
[2] 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).
[3] J.R. Kuttler undV.G. Sigillito,Inequalities for Membrane and Stekloff Eigenvalues, J. Math. anal. Appl.23, 148–160 (1968). · Zbl 0167.45701
[4] L.E. Payne,Some Isoperimetric Inequalities for Harmonic Functions (Forschungsinstitut für Mathematik, ETH Zürich). · Zbl 0289.31006
[5] L.E. Payne,Isoperimetric Inequalities and Their Applications, SIAM Rev.9, No. 3, 453–488 (Juli 1967). · Zbl 0154.12602
[6] J. Hersch undL.E. Payne,One-Dimensional Auxiliary Problems and a priori Bounds, Abhandlungen Math. Seminar Univ. Hamburg, Band 36, p. 57–65 (Juli 1971). · Zbl 0214.35905
[7] G. Pólya undM. Schiffer,Convexity of Functionals by Transplantation, J. Anal. Math.3, 245–345 (1954). · Zbl 0056.32701
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