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
Access Full Article
topHow to cite
topDacorogna, 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
top- [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] Ball ( J.M.) .— Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal.64 (1977), pp. 337-403. Zbl0368.73040MR475169
- [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] Ciarlet ( P.) .- Mathematical elasticity, Vol. 1, North Holland, 1987. Zbl0648.73014
- [5] Dacorogna ( B.) .— Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989. Zbl0703.49001MR990890
- [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] Iwaniec ( T.) and Lutoborski ( A.) .— Integral estimates for null Lagrangians, to appear in Arch. Rational Mech. Anal. Zbl0793.58002MR1241286
- [8] Morrey ( C.B.) .- Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. Zbl0142.38701MR202511
- [9] Sverak ( V.) .- Quasiconvex functions with subquadratic growth, Proc. Roy. Soc. LondonA433 (1991), pp. 723-725. Zbl0741.49016MR1116970
- [10] Sverak ( V.) .- Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh120A (1992), pp. 185-189. Zbl0777.49015MR1149994
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.