Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
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  • [1] Rayleigh, Theory of sound, Vol. I, Dover, 1945. MR 0016009
  • [2] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Camb. Univ. Press, 1934.
  • [3] G. Polya, and G. Szegö, Isoperimetric inequalities in mathematical physics, Princeton U. Press, 1951. MR 0043486
  • [4] 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.
  • [5] E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. 94, 97-100 (1924).
  • [6] 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.
  • [7] G. N. Watson, A treatise on the theory of Bessel functions (Second edition), Camb. Univ. Press, 1948. MR 0010746

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DOI: https://doi.org/10.1090/qam/62313
Article copyright: © Copyright 1954 American Mathematical Society

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