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Über das Stekloffsche Eigenwertproblem: Isoperimetrische Ungleichungen für symmetrische Gebiete

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Summary

Isoperimetric inequalities ofPólya [6] for symmetric membranes are extended to the Stekloff problem. The given symmetric domainG z is mapped conformally onto a circle; some (harmonic) eigenfunctions of the circle are transplanted ontoG z ; application of Rayleigh's and Poincaré's principles to the transplanted functions gives upper bounds for a number of eigenvalues ofG z which depends on the order of symmetry of the domain.

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Literaturverzeichnis

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Authors and Affiliations

  1. Mathematisches Institute der ETH, 8006, Zürich

    Catherine Bandle

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  1. Catherine Bandle
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Bandle, C. Über das Stekloffsche Eigenwertproblem: Isoperimetrische Ungleichungen für symmetrische Gebiete. Journal of Applied Mathematics and Physics (ZAMP) 19, 627–637 (1968). https://doi.org/10.1007/BF01594970

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  • DOI: https://doi.org/10.1007/BF01594970

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