Randwertprobleme und Methode der inneren Parallelen: eine gemeinsame Erweiterung zweier Ungleichungen von Pólya

  • Panagiotis Chatzidimou
  • Joseph Hersch
Original Papers


Die „Methode der inneren Parallelen“ von Makai und Pólya wird hier auf das Randwertproblem (3) angewendet. Die sich ergebenden Schranken (11) und (11′) für das FunktionalQ(α) enthalten als Grenzfälle die von Pólya [9] erhaltenen Schranken (2) und (1) für die Torsionssteifigkeit (Fallα=0) bzw. für den Grundton einer Membran (Fallαλ1.


We apply here the “method of interior parallels” of Makai and Pólya to the boundary value problem (3). The resulting bounds (11) and (11′) for the functionalQ(α) contain as limit cases the bounds (2) and (1) obtained by Pólya [9] for torsional rigidity (caseα=0) and for the lowest eigenfrequency of a membrane (caseαλ1).


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Copyright information

© Birkhäuser Verlag Basel 1984

Authors and Affiliations

  • Panagiotis Chatzidimou
    • 1
  • Joseph Hersch
    • 1
  1. 1.Eidg. Technische HochschuleZürich

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