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On inequalities of Korn’s type. I: Boundary-value problems for elliptic systems of partial differential equations. (English) Zbl 0193.39001

MSC:
35J58 Boundary value problems for higher-order elliptic systems
35J25 Boundary value problems for second-order elliptic equations
35J20 Variational methods for second-order elliptic equations
35D30 Weak solutions to PDEs
49J40 Variational inequalities
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References:
[1] Nečas, J., Les méthodes directes en théorie des équations elliptiques. Prague: Academia 1967.
[2] Nečas, J., Sur les normes équivalentes dans W p (k) ({\(\Omega\)})et sur la coercitivité des formes formellement positives. Les presses de l’Université de Montréal, Janvier 1966, 102–128.
[3] Korn, A., Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen. Bull. Int. Cracovie Akad. Umiejet, Classe des sc. math. et nat. (1909). · JFM 40.0884.02
[4] Friedrichs, K. O., On the boundary-value problems of the theory of elasticity and Korn’s inequality. Annals of Math. 48, 2 (1947). · Zbl 0029.17002
[5] Eydus, D. M., On the mixed problem of the theory of elasticity. Dokl. A. N. SSSR 76, 2 (1951) [Russian].
[6] Payne, L. E., & H. F. Weinberger, On Korn’s inequality. Arch. Rational Mech. Anal. 8, 89–98 (1961). · Zbl 0107.31105
[7] Gobert, J., Une inégalité fondamentale de la théorie de l’élasticité. Bull. Soc. Royale des Sciences de Liège 3–4 (1962).
[8] Besov, O. V., On the coerciveness in the anisotropic Sobolev space. Matem. Sbornik 73, 115, 4, 585–599 (1967) [Russian].
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