Another approach to linearized elasticity and a new proof of Korn's inequality

Mathematical Models and Methods in Applied Sciences

Volumn 15, Issue 2, 2005, Pages 259-271

  Ciarlet, Philippe G ^a   Ciarlet Jr , Patrick ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b ENSTA PARISTECH   (France)

Author keywords

Korn's inequality; St Venant compatibility conditions; Three dimensional linearized elasticity

Indexed keywords

EID: 12844252658     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202505000352     Document Type: Article

References (17)

1. R. A. Adams, Sobolev Spaces (Academic Press, 1975).
2. C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czech. Math. J. 44 (1994) 109-140.
3. P. G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity (North-Holland, 1988).
4. P. G. Ciarlet and P. Ciarlet, Jr., Another approach to linearized elasticity and Korn's inequality, C. R. Acad. Sci. Paris, Ser. I 339 (2004) 307-312.
5. P. G. Ciarlet and F. Laurent, Continuity of a deformation as a function of its Cauchy-Green tensor, Arch. Rational Mech. Anal. 167 (2003) 255-269.
6. P. G. Ciarlet and C. Mardare, On rigid and infinitesimal rigid displacements in three-dimensional elasticity, Math. Mod. Meth. Appl. Sci. 13 (2003) 1589-1598.
7. 1-norm of their Cauchy-Green tensors, C. R. Acad. Sci. Paris, Ser. I 338 (2004) 505-510.
8. P. G. Ciarlet and C. Mardare, Recovery of a manifold with boundary and its continuity as a function of its metric tensor, J. Math. Pures Appl. 83 (2004) 811-843.
9. P. Ciarlet, Jr., Potentials of vector fields in Lipschitz domains, to appear.
10. G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique (Dunod, 1972); English translation: Inequalities in Mechanics and Physics (Springer-Verlag, 1976).
11. G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique (Dunod, 1972); English translation: Inequalities in Mechanics and Physics (Springer-Verlag, 1976).
12. 3, J. Fac. Sci. Univ. Tokyo, Sec. 1A, Math. 39 (1992) 279-307.
13. V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations (Springer-Verlag, 1986).
14. J. Nečas, Les Méthodes Directes en Théorie des Equations Elliptiques (Masson, 1967).
15. L. Schwartz, Cours d'Analyse, Deuxième Partie (Ecole Polytechnique, 1959).
16. n and their metric tensors, Siberian Math. J. 44 (2003) 332-345.
17. T. W. Ting, St. Venant's compatibility conditions, Tensor, N. S. 28 (1974) 5-12.