References
Korn, A., Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen. Bull. Intern. Cracov. Akad. Umiejet (Classe Sci. Math. Nat.) 705–724 (1909).
Friedrichs, K. O., On certain inequalities and characteristic value problems for analytic functions and for functions of two variables. Trans. Amer. Math. Soc. 41, 321–364 (1937).
Friedrichs, K. O., On the boundary-value problems of the theory of elasticity and Korn's inequality. Ann. of Math. 48, 441–471 (1947).
Bernstein, B., & R. A. Toupin, Korn inequalities for the sphere and circle. Arch. Rational Mech. Anal. 6, 51–64 (1960).
Payne, L. E., & H. F. Weinberger, On Korn's inequality. Arch. Rational Mech. Anal. 8, 89–98 (1961).
Dafermos, C. M., Some remarks on Korn's inequality. Z. Angew. Math. Phys. 19, 913–920 (1968).
Hlaváček, I., & J. Nečas, On inequalities of Korn's type. Part I and II. Arch. Rational Mech. Anal. 36, 305–334 (1970).
Horgan, C. O., & J. K. Knowles, Eigenvalue problems associated with Korn's inequalities. Arch. Rational Mech. Anal. 40, 384–402 (1971).
Fichera, G., Existence theorems in elasticity; Boundary value problems of elasticity with unilateral constraints, Handbuch der Physik, S. Flügge and C. Truesdell eds., Vol. 6a/2, pp. 347–424. Springer-Verlag, Berlin, Heidelberg, New York 1972.
Gurtin, M. E., The linear theory of elasticity, Handbuch der Physik, S. Flügge and C. Truesdell eds., Vol. 6a/2, pp. 1–295. Springer-Verlag, Berlin, Heidelberg, New York 1972.
Knops, R. J., & E. W. Wilkes, Theory of elastic stability, Handbuch der Physik, S. Flügge and C. Truesdell eds., Vol. 6a/3, pp. 125–302. Springer-Verlag, Berlin, Heidelberg, New York 1973.
Horgan, C. O., On Korn's inequality for incompressible media. SIAM J. Appl. Math. 28, 419–430 (1975).
Horgan, C. O., Inequalities of Korn and Friedrichs in elasticity and potential theory. Z. Angew. Math. Phys. 26, 155–164 (1975).
Villaggio, P., Qualitative Methods in Elasticity. Noordhoff, Leyden, 1977.
Babuška, I., & A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. K. Aziz ed., 5–359. Academic Press, New York, 1972.
Oden, J. T., & J. N. Reddy, Variational Methods in Theoretical Mechanics. Springer-Verlag, Berlin, Heidelberg, New York 1976.
Ciarlet, P. G., The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.
Toupin, R. A., Saint-Venant's principle. Arch. Rational Mech. Anal. 18, 83–96 (1965).
Berdichevskii, V. L., On the proof of the Saint-Venant principle for bodies of arbitrary shape. J. Appl. Math. Mech. 38, 799–813 (1975).
Horgan, C. O., & J. K. Knowles, Recent developments concerning Saint-Venant's principle, Advances in Applied Mechanics, J. W. Hutchinson ed., Vol. 23, Chapter 3, Academic Press, New York, 1983.
Ladyzhenskaya, O. A., & V. A. Solonnikov, Some problems of vector analysis and generalized formulations of boundary-value problems for the Navier-Stokes equations. J. Soviet Math. 10, 257–286 (1978).
Horgan, C. O., & L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow. SIAM J. Appl. Math. 35, 97–116 (1978).
Nitsche, J. A., On Korn's second inequality. R.A.I.R.O. J. of Numerical Analysis 15, 237–248 (1981).
Mikhlin, S. G., Variational Methods in Mathematical Physics (translated by T. Boddington). Macmillan, New York, 1964.
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Horgan, C.O., Payne, L.E. On inequalities of Korn, Friedrichs and Babuška-Aziz. Arch. Rational Mech. Anal. 82, 165–179 (1983). https://doi.org/10.1007/BF00250935
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DOI: https://doi.org/10.1007/BF00250935