Two-dimensional examples of rank-one convex functions that are not quasiconvex

• Autorzy: M. K. Benaouda , J. J. Telega
• Języki publikacji: EN

Abstrakty

EN

The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.

Słowa kluczowe

EN

rank-one convex function; quasiconvexity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 73
• Numer: 3
• Strony: 291-295

Daty

wydano

2000

otrzymano

1999-12-13

Twórcy

autor

M. K. Benaouda

• Université des Sciences et, Technologies de Lille, Avenue Paul Langevin, 59655 Villeneuve d'Ascq, France

autor

J. J. Telega

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland

Bibliografia

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• [3] P. G. Ciarlet, Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity, North-Holland, Amsterdam, 1988.
• [4] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, Berlin, 1989.
• [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.
• [6] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966.
• [7] P. Pedregal, Parametrized Measures and Variational Principles, Birkhäuser, Basel, 1997.
• [8] V. Šverák, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), 185-189.