The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.
@article{bwmeta1.element.bwnjournal-article-apmv73z3p291bwm, author = {Benaouda, M. and Telega, J.}, title = {Two-dimensional examples of rank-one convex functions that are not quasiconvex}, journal = {Annales Polonici Mathematici}, volume = {75}, year = {2000}, pages = {291-295}, zbl = {1055.49505}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv73z3p291bwm} }
Benaouda, M.; Telega, J. Two-dimensional examples of rank-one convex functions that are not quasiconvex. Annales Polonici Mathematici, Tome 75 (2000) pp. 291-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv73z3p291bwm/
[000] [1] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. | Zbl 0565.49010
[001] [2] J. M. Ball and F. Murat, -quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225-253. | Zbl 0549.46019
[002] [3] P. G. Ciarlet, Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity, North-Holland, Amsterdam, 1988. | Zbl 0648.73014
[003] [4] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, Berlin, 1989. | Zbl 0703.49001
[004] [5] B. Dacorogna and J. P. Haeberly, Remarks on a numerical study of convexity, quasiconvexity, and rank-one convexity, in: Progr. Nonlinear Differential Equations Appl. 25, Birkhäuser, Basel, 1996, 143-154. | Zbl 0898.49012
[005] [6] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966.
[006] [7] P. Pedregal, Parametrized Measures and Variational Principles, Birkhäuser, Basel, 1997.
[007] [8] V. Šverák, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), 185-189. | Zbl 0777.49015