A relaxation theorem in the space of functions of bounded deformation

Ana Cristina Barroso; Irene Fonseca; Rodica Toader

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 1, page 19-49
  • ISSN: 0391-173X

How to cite

top

Barroso, Ana Cristina, Fonseca, Irene, and Toader, Rodica. "A relaxation theorem in the space of functions of bounded deformation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.1 (2000): 19-49. <http://eudml.org/doc/84402>.

@article{Barroso2000,
author = {Barroso, Ana Cristina, Fonseca, Irene, Toader, Rodica},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {relaxation; special functions of bounded deformation; quasiconvexity; Poincaré type inequality},
language = {eng},
number = {1},
pages = {19-49},
publisher = {Scuola normale superiore},
title = {A relaxation theorem in the space of functions of bounded deformation},
url = {http://eudml.org/doc/84402},
volume = {29},
year = {2000},
}

TY - JOUR
AU - Barroso, Ana Cristina
AU - Fonseca, Irene
AU - Toader, Rodica
TI - A relaxation theorem in the space of functions of bounded deformation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 1
SP - 19
EP - 49
LA - eng
KW - relaxation; special functions of bounded deformation; quasiconvexity; Poincaré type inequality
UR - http://eudml.org/doc/84402
ER -

References

top
  1. [1] L. Ambrosio - A. Coscia - G. Dal Maso, Fine properties of functions with bounded deformation, Arch. Rat. Mech. Anal.139 (1997), 201-238. Zbl0890.49019MR1480240
  2. [2] L. Ambrosio - G. Dal Maso, On the relaxation in B V (Ω; R m) of quasi-convex integrals, J. Funct. Anal.109 (1992), 76-97. Zbl0769.49009
  3. [3] L. Ambrosio - S. Mortola - V.M. Tortorelli, Functionals with linear growth defined on vector valued B V functions, J. Math. Pures et Appl.70 (1991), 269-323. Zbl0662.49007MR1113814
  4. [4] A.C. Barroso - G. Bouchitté - G. Buttazzo - I. Fonseca, Relaxation of bulk and interfacial energies, Arch. Rat. Mech. Anal.135 (1996), 107-173. Zbl0876.49037MR1418463
  5. [5] G. Bellettini - A. Coscia - G. Dal Maso, Special functions of bounded deformation, Math. Z.228 (1998), 337-351. Zbl0914.46007MR1630504
  6. [6] A. Braides - A. Defranceschi - E. Vitali, A relaxation approach to Hencky's plasticity, Appl. Math. Optimization35 (1997), 45-68. Zbl0860.49014MR1418263
  7. [7] G. Bouchitté - I. Fonseca - L. Mascarenhas, A global method for relaxation, Arch. Rat. Mech. Anal.145 (1998), 51-98. Zbl0921.49004MR1656477
  8. [8] B. Dacorogna, "Direct Methods in the Calculus of Variations ", Springer, 1989. Zbl0703.49001MR990890
  9. [9] F.B. Ebobisse, On lower semicontinuity of integral functionals in LD(Q), Ricerche Mat. (to appear). Zbl1027.49014MR1795030
  10. [10] I. Fonseca - S. Müller, Quasiconvex integrands and lower semicontinuity in L1, SIAM J. Math. Anal.23 (1992), 1081-1098. Zbl0764.49012MR1177778
  11. [11] I. Fonseca - S. Muller, Relaxation of quasiconvex functionals in B V (Ω; Rp), Arch. Rat. Mech. Anal.123 (1993), 1-49. Zbl0788.49039
  12. [12] I. Fonseca - S. Müller, A-quasiconvexity, lower semicontinuity and Young measures, SIAM J. Math. Anal.30 (1999), 1355-1390. Zbl0940.49014MR1718306
  13. [13] R.V. Kohn, "New Estimates for Deformations in Terms of Their Strains", Ph.D. Thesis, Princeton University, 1979. 
  14. [14] H. Matthies - G. Strang - E. Christiansen, "The Saddle Point of a Differential Program", Energy Methods in Finite Element Analysis, Wiley, New York, 1979. MR537013
  15. [15] D.A. Ornstein, Non-inequality for differential operators in the L1 -norm, Arch. Rat. Mech. Anal.11 (1962), 40-49. Zbl0106.29602MR149331
  16. [16] Y.G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math. J.9 (1968), 1039-1045 (translation of Sibirsk. Mat. Z. 9 (1968), 1386-1394). Zbl0169.18301MR240274
  17. [17] P.M. Suquet, Existence et régularité des solutions des équations de la plasticité parfaite, C. R. Acad. Sci. Paris Sér. A286 (1978), 1201-1204. Zbl0378.35057MR501114
  18. [18] P.M. Suquet, Un espace fonctionel pour les équations de la plasticité, Ann. Fac. Sci. Toulouse Math (6) 1 (1979), 77-87. Zbl0405.46027MR533600
  19. [19] R. Temam, "Problèmes Mathématiques en Plasticité", Gauthier-Villars, 1983. Zbl0547.73026MR711964
  20. [20] R. Temam - G. Strang, Functions of bounded deformation, Arch. Rat. Mech. Anal.75 (1980), 7-21. Zbl0472.73031MR592100

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.