Symmetric tensor fields of bounded deformation

Annali di Matematica Pura ed Applicata

Volumn 192, Issue 5, 2013, Pages 815-851

  Bredies, Kristian ^a  

^a UNIVERSITY OF GRAZ   (Austria)

Author keywords

Boundary traces; Bounded deformation; Continuous compact embeddings; Sobolev Korn inequality; Symmetric tensor fields

Indexed keywords

EID: 84884699419     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-011-0248-4     Document Type: Article

References (16)

1. Ambrosio L., Fusco N., Pallara D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000).
2. Anzellotti G., Giaquinta M.: Existence of the displacements field for an elasto-plastic body subject to Hencky's law and Von Mises yield condition. Manuscripta Math. 32, 101-136 (1980). doi: 10. 1007/BF01298185.
3. Biggs N.: Algebraic Graph Theory, 2nd edn. Cambridge University Press, Cambridge (1993).
4. Bredies K., Kunisch K., Pock T.: Total generalized variation. SIAM J. Imaging Sci. 3(3), 492-526 (2010).
5. Bredies, K., Valkonen, T.: Inverse problems with second-order total generalized variation constraints. In: Proceedings of the 9th International Conference on Sampling Theory and Applications (2011).
6. Chang C. S., Gao J.: Second-gradient constitutive theory for granular material with random packing structure. Int. J. Solids Struct. 32(16), 2279-2293 (1995).
7. Dunford N. J., Schwartz J. T.: Linear Operators. Part I: General Theory, Pure and Applied Mathematics. Wiley, New York (1958).
8. Evans L. C., Gariepy R. F.: Measure Theory and Fine Properties of Functions. CRC Press, UK (1992).
9. Gargiulo G., Zappale E.: A lower semicontinuity result in SBD. J. Convex Anal. 15(1), 191-200 (2008).
10. Godsil C., Royle G.: Algebraic Graph Theory. Springer, New York (2001).
11. Kikuchi N., Oden J. T.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1988).
12. Schwartz L.: Theorie des Distributions, Publications de l'institut de Mathematique de l'universite de Strasbourg. Hermann, Paris (1966).
13. Strauss, M. J.: Variations of Korn's and Sobolev's equalities. In: Partial Differential Equations. (Proceedings of Symposia in Pure Mathematics, vol. XXIII, University of California, Berkeley 1971), pp. 207-214. American Mathematical Society, Providence (1973).
14. Suiker A. S. J., Chang C. S.: Application of higher-order tensor theory for formulating enhanced continuum models. Acta Mech. 142, 223-234 (2000). doi: 10. 1007/BF01190020.
15. Temam R.: Mathematical Problems in Plasticity. Bordas, Paris (1985).
16. Temam R., Strang G.: Functions of bounded deformation. Arch. Ration. Mech. Anal. 75(1), 7-21 (1980).