On the different notions of convexity for rotationally invariant functions

Bernard Dacorogna; Hideyuki Koshigoe

Annales de la Faculté des sciences de Toulouse : Mathématiques (1993)

  • Volume: 2, Issue: 2, page 163-184
  • ISSN: 0240-2963

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Dacorogna, Bernard, and Koshigoe, Hideyuki. "On the different notions of convexity for rotationally invariant functions." Annales de la Faculté des sciences de Toulouse : Mathématiques 2.2 (1993): 163-184. <http://eudml.org/doc/73317>.

@article{Dacorogna1993,
author = {Dacorogna, Bernard, Koshigoe, Hideyuki},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {rotationally invariant functions; convexity conditions; rank-one convexity; quasi-convexity; polyconvexity},
language = {eng},
number = {2},
pages = {163-184},
publisher = {UNIVERSITE PAUL SABATIER},
title = {On the different notions of convexity for rotationally invariant functions},
url = {http://eudml.org/doc/73317},
volume = {2},
year = {1993},
}

TY - JOUR
AU - Dacorogna, Bernard
AU - Koshigoe, Hideyuki
TI - On the different notions of convexity for rotationally invariant functions
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1993
PB - UNIVERSITE PAUL SABATIER
VL - 2
IS - 2
SP - 163
EP - 184
LA - eng
KW - rotationally invariant functions; convexity conditions; rank-one convexity; quasi-convexity; polyconvexity
UR - http://eudml.org/doc/73317
ER -

References

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  1. [1] Alibert ( J.J.) and Dacorogna ( B.) .— An example of a quasiconvex function that is not polyconvex in two dimensions, Arch. Rational Mech. Anal.117 (1992), pp. 155-166. Zbl0761.26009MR1145109
  2. [2] Ball ( J.M.) .— Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal.64 (1977), pp. 337-403. Zbl0368.73040MR475169
  3. [3] Buttazzo ( G.), Dacorogna ( B.) and Gangbo ( W.) .— On the envelopes of functions depending on singular values of matrices, to appear in Boll. Unione Mat. Italiana. Zbl0803.49014MR1274317
  4. [4] Ciarlet ( P.) .- Mathematical elasticity, Vol. 1, North Holland, 1987. Zbl0648.73014
  5. [5] Dacorogna ( B.) .— Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989. Zbl0703.49001MR990890
  6. [6] Dacorogna ( B.), Douchet ( J.), Gangbo ( W.) and Rappaz ( J.) .— Some examples of rank one convex functions in dimension two, Proc. Roy. Soc. Edinburgh114A (1990), pp. 135-150. Zbl0722.49018MR1051612
  7. [7] Iwaniec ( T.) and Lutoborski ( A.) .— Integral estimates for null Lagrangians, to appear in Arch. Rational Mech. Anal. Zbl0793.58002MR1241286
  8. [8] Morrey ( C.B.) .- Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. Zbl0142.38701MR202511
  9. [9] Sverak ( V.) .- Quasiconvex functions with subquadratic growth, Proc. Roy. Soc. LondonA433 (1991), pp. 723-725. Zbl0741.49016MR1116970
  10. [10] Sverak ( V.) .- Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh120A (1992), pp. 185-189. Zbl0777.49015MR1149994

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