On Korn's second inequality

J. A. Nitsche

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 3, page 237-248
  • ISSN: 0764-583X

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Nitsche, J. A.. "On Korn's second inequality." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 15.3 (1981): 237-248. <http://eudml.org/doc/193380>.

@article{Nitsche1981,
author = {Nitsche, J. A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Korn's second inequality; boundary of the domain},
language = {eng},
number = {3},
pages = {237-248},
publisher = {Dunod},
title = {On Korn's second inequality},
url = {http://eudml.org/doc/193380},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Nitsche, J. A.
TI - On Korn's second inequality
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 3
SP - 237
EP - 248
LA - eng
KW - Korn's second inequality; boundary of the domain
UR - http://eudml.org/doc/193380
ER -

References

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  1. [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). Zbl0383.65058MR520174
  2. [2] G. DUVAUT and J. L. LIONS, Les Inéquations en Mécanique et en Physique, Dunod, Paris (1972). Zbl0298.73001MR464857
  3. [3] G. FICHERA, Linear Elliptic Differential Systems and Eigenvalue Problems. Springer-Verlag, Berlin-Heidelberg-New York (1965). Zbl0138.36104MR209639
  4. [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. [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. Zbl0029.17002MR22750
  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. Zbl39.0853.03JFM39.0853.03
  7. [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. Zbl40.0884.02JFM40.0884.02
  8. [8] L. E. PAYNE and H. F. WEINBERGER, On korn's inequality. Arch. Rational Mech. Anal., 8, (1961), 89-98. Zbl0107.31105MR158312
  9. [9] E. M. STEIN, Singular integrals and differentiability properties of functions. Princeton Univ. Press, Princeton, N. J. (1970). Zbl0207.13501MR290095
  10. [10] W. VELTE, Direkte Methoden der Variationsrechnung. . B. G. Teubner, Stuttgart (1976). Zbl0333.49035MR500387

Citations in EuDML Documents

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  1. Florian Theil, Surface energies in a two-dimensional mass-spring model for crystals
  2. E. Bécache, T. Ha Duong, A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem
  3. Eduard Feireisl, Šárka Matušů-Nečasová, The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics
  4. Florian Theil, Surface energies in a two-dimensional mass-spring model for crystals
  5. A. Bamberger, P. Joly, M. Kern, Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section
  6. L. Desvillettes, Cédric Villani, On a variant of Korn's inequality arising in statistical mechanics
  7. L. Desvillettes, Cédric Villani, On a variant of Korn’s inequality arising in statistical mechanics
  8. Ivan Hlaváček, Inequalities of Korn's type, uniform with respect to a class of domains
  9. J. Haslinger, P. Neittaanmäki, Shape optimization in contact problems. Approximation and numerical realization
  10. Lynn Schreyer Bennethum, Xiaobing Feng, A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element

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