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Elliptical membranes with smallest second eigenvalue. (English) Zbl 0271.35018


MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P05 General topics in linear spectral theory for PDEs
74K15 Membranes
70J10 Modal analysis in linear vibration theory
35J25 Boundary value problems for second-order elliptic equations
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References:

[1] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. · Zbl 0171.38503
[2] P. R. Garabedian and M. Schiffer, Variational problems in the theory of elliptic partial differential equations, J. Rational Mech. Anal. 2 (1953), 137 – 171. · Zbl 0050.10002
[3] L. E. Payne, Isoperimetric inequalities and their applications, SIAM Rev. 9 (1967), 453 – 488. · Zbl 0154.12602 · doi:10.1137/1009070
[4] G. Pólya, On the characteristic frequencies of a symmetric membrane, Math. Z. 63 (1955), 331 – 337. · Zbl 0065.08703 · doi:10.1007/BF01187944
[5] John William Strutt Rayleigh Baron, The Theory of Sound, Dover Publications, New York, N. Y., 1945. 2d ed. · Zbl 0061.45904
[6] B. A. Troesch and H. R. Troesch, Eigenfrequencies of an elliptic membrane, Math. Comput. 27 (1973), 755 – 765. · Zbl 0271.35017
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