Archive for Rational Mechanics and Analysis

, Volume 5, Issue 1, pp 286–292 | Cite as

An optimal Poincaré inequality for convex domains

  • L. E. Payne
  • H. F. Weinberger
Article

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References

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    Courant, R., & D. Hilbert: Methoden der Mathematischen Physik, vol. 1. Berlin: Springer 1931.Google Scholar
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    Kornhauser, E. T., & I. Stakgold: A Variational Theorem for b<2 u + λu = 0 and its Applications. J. Math. Phys. 31, 45–54 (1952). (See also Pólya, G.: Remarks on the Foregoing Paper. J. Math. Phys. 31, 55–57 (1952).)MathSciNetGoogle Scholar
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    Payne, L. E., & H. F. Weinberger: New Bounds for Solutions of Second Order Elliptic Partial Differential Equations. Pac. J. of Math. 8, 551–573 (1958).MathSciNetGoogle Scholar
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    Payne, L. E., & H. F. Weinberger: Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and Plates. J. Soc. Indust. Appl. Math. 5, 17–182 (1957).MathSciNetCrossRefGoogle Scholar
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    Szegö, G.: Inequalities for Certain Membranes of a Given Area. J. Rational Mech. Anal. 3, 343–356 (1954).MATHMathSciNetGoogle Scholar
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    Weinberger, H. F.: An Isoperimetric Inequality for the N-dimensional Free Membrane Problem. J. Rational Mech. Anal. 5, 633–636 (1956).MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1960

Authors and Affiliations

  • L. E. Payne
    • 1
  • H. F. Weinberger
    • 1
  1. 1.Institute for Fluid Dynamics and Applied Mathematics University of MarylandCollege Park

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