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Obere Schranken für die Eigenwerte einer stückweise freien Membran auf einem «Vierseit»

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Summary

Using Poincaré's principle and the harmonic transplantation [3], upper bounds for the partially free membranes are constructed. The bounds for the first eigenvalue are isoperimetric; the extremal domain is the rectangle. Extensions to more general eigenvalue problems are indicated.

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Literatur

  1. C. Bandle,Konstruktion isoperimetrischer Ungleichungen der mathematischen Physik aus solchen der Geometrie (zu erscheinen in den Commentarii Math. Helv.).

  2. R. Courant undD. Hilbert,Methods of Mathematical Physics, Bd. II (New York 1965).

  3. J. Hersch,Transplantation harmonique, transplantation par modules, et théorèmes isopérimétriques, Commentarii Math. Helv.44, 354 (1969).

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  4. L. E. Payne undH. F. Weinberger,An Optimal Poincaré Inequality for Convex Domains, Arch. ration. Mech. Anal.5, 286 (1960).

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  5. G. Pólya undG. Szegö,Isoperimetric Inequalities in Mathematical Physics (Princeton 1951).

  6. G. Szegö,Inequalities for Certain Eigenvalues of a Membrane of Given Area, J. ration. Mech. Anal.3, 343 (1954).

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  7. O. Teichmüller,Untersuchungen über konforme und quasikonforme Abbildungen, Deutsche Mathematik3, 621 (1938).

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Authors and Affiliations

  1. Institut Battelle, Carouge-Genève

    Catherine Bandle

Authors
  1. Catherine Bandle
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Bandle, C. Obere Schranken für die Eigenwerte einer stückweise freien Membran auf einem «Vierseit». Journal of Applied Mathematics and Physics (ZAMP) 21, 1072–1077 (1970). https://doi.org/10.1007/BF01594863

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  • DOI: https://doi.org/10.1007/BF01594863

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