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On Korn's inequality

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References

  1. Bernstein, B., & R. Toupin: Korn inequalities for the sphere and for the circle. Arch. Rational Mech. Anal. 6, No. 1, 51–64 (1960).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Courant, R., & D. Hilbert: Methoden der mathematischen Physik, Vol. 2. Berlin: Springer 1937.

    Google Scholar 

  3. Friedrichs, K. O.: On the boundary-value problems of the theory of elasticity and Korn's inequality. Ann. of Math. 48, 441–471 (1947).

    Article  MathSciNet  Google Scholar 

  4. Korn, A.: Solution générale du problème d'équilibre dans la théorie de l'élasticité, dans le case où les efforts sont données à la surface. Annales de la faculté des sciences de Toulouse, ser. 2, 10, 165–269 (1908).

    MathSciNet  Google Scholar 

  5. Korn, A.: Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen. Bulletin Internationale, Cracovie Akademie Umiejet, Classe des sciences mathématiques et naturelles 1909, pp. 705–724.

  6. Love, A. E. H.: A Treatise on the Mathematical Theory of Elasticity. 1927.

  7. Payne, L. E., & H. F. Weinberger: New bounds in harmonic and biharmonic problems. J. Math. Phys. 33, 291–307 (1955).

    MATH  MathSciNet  Google Scholar 

  8. Payne, L. E., & H. F. Weinberger: New bounds for solutions of second order elliptic partial differential equations. Pacific J. Math. 8, No. 3, 551–573 (1958).

    MATH  MathSciNet  Google Scholar 

  9. Synge, J. L., & A. Schild: Tensor Calculus. Toronto 1949.

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Authors and Affiliations

  1. University of Maryland, College Park, Maryland

    L. E. Payne & H. F. Weinberger

  2. University of Minnesota, Minneapolis, Minnesota

    L. E. Payne & H. F. Weinberger

Authors
  1. L. E. Payne
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  2. H. F. Weinberger
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Additional information

Communicated by R. A. Toupin

This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 49(638)228, and by the Office of Naval Research under Contract Nonr 710(16) (NR 044004).

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Payne, L.E., Weinberger, H.F. On Korn's inequality. Arch. Rational Mech. Anal. 8, 89–98 (1961). https://doi.org/10.1007/BF00277432

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  • DOI: https://doi.org/10.1007/BF00277432

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