On Korn’s second inequality. (English) Zbl 0467.35019


35B45 A priori estimates in context of PDEs
35J40 Boundary value problems for higher-order elliptic equations
Full Text: DOI EuDML


[1] P. G. CIARLET, The Finite Element Method for Elliptic Problems. Studies in Mathematics and its Applications. North-Holland Publ. Comp., Amsterdam-New York- Oxford (1978). Zbl0383.65058 MR520174 · Zbl 0383.65058
[2] G. DUVAUT and J. L. LIONS, Les Inéquations en Mécanique et en Physique, Dunod, Paris (1972). Zbl0298.73001 MR464857 · Zbl 0298.73001
[3] G. FICHERA, Linear Elliptic Differential Systems and Eigenvalue Problems. Springer-Verlag, Berlin-Heidelberg-New York (1965). Zbl0138.36104 MR209639 · Zbl 0138.36104 · doi:10.1007/BFb0079959
[4] G. FICHERA, Existence theorems in elasticity-boundary value problems of elasticity with unilateral constraints. Encyclopedia of Physics (S. Flügge, Chief Editor), Vol. VIa/2 : Mechanics of Solids II (C. Truesdell, Editor), pp. 347-424, Springer-Verlag, Berlin (1972).
[5] K. O. FRIEDRICHS, On the boundary value problems of the theory of elasticity and Korn’s inequality. Ann. of Math., 48, (1947), 441-471. Zbl0029.17002 MR22750 · Zbl 0029.17002 · doi:10.2307/1969180
[6] [6] A. KORN, Solution générale du problème d’équilibre dans la théorie de l’élasticité dans le cas où les efforts sont donnés à la surface. . Ann. Université Toulouse (1908), 165-269. Zbl39.0853.03 JFM39.0853.03
[7] A. KORN, Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen. Bull. Intern. Cracov. Akad. umiejet (Classe Sci. Math. nat.) (1909) 706-724. JFM40.0884.02
[8] L. E. PAYNE and H. F. WEINBERGER, On korn’s inequality. Arch. Rational Mech. Anal., 8, (1961), 89-98. Zbl0107.31105 MR158312 · Zbl 0107.31105 · doi:10.1007/BF00277432
[9] E. M. STEIN, Singular integrals and differentiability properties of functions. Princeton Univ. Press, Princeton, N. J. (1970). Zbl0207.13501 MR290095 · Zbl 0207.13501
[10] W. VELTE, Direkte Methoden der Variationsrechnung. . B. G. Teubner, Stuttgart (1976). Zbl0333.49035 MR500387 · Zbl 0333.49035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.