Lowest eigenvalues of nearly circular regions
Authors:
Herbert B. Keller and Joseph B. Keller
Journal:
Quart. Appl. Math. 12 (1954), 141-150
MSC:
Primary 36.0X
DOI:
https://doi.org/10.1090/qam/62313
MathSciNet review:
62313
Full-text PDF Free Access
References |
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Additional Information
- John William Strutt Rayleigh Baron, The Theory of Sound, Dover Publications, New York, N. Y., 1945. 2d ed. MR 0016009
G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Camb. Univ. Press, 1934.
- G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, No. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486
G. Faber, Beweis dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Sitzungsberiche, Bayr. Ak. Wiss, 1923, 169-172.
E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. 94, 97-100 (1924).
H. B. Keller and J. B. Keller, Eigenvalues of nearly circular wave-guides, Res. Rpt. TW-17, NYU, Math. Res. Grp., Wash. Sq. College of Arts and Sci., 1952.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
Rayleigh, Theory of sound, Vol. I, Dover, 1945.
G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Camb. Univ. Press, 1934.
G. Polya, and G. Szegö, Isoperimetric inequalities in mathematical physics, Princeton U. Press, 1951.
G. Faber, Beweis dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Sitzungsberiche, Bayr. Ak. Wiss, 1923, 169-172.
E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. 94, 97-100 (1924).
H. B. Keller and J. B. Keller, Eigenvalues of nearly circular wave-guides, Res. Rpt. TW-17, NYU, Math. Res. Grp., Wash. Sq. College of Arts and Sci., 1952.
G. N. Watson, A treatise on the theory of Bessel functions (Second edition), Camb. Univ. Press, 1948.
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Article copyright:
© Copyright 1954
American Mathematical Society
