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

M. Benaouda; J. Telega

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 3, page 291-295
  • ISSN: 0066-2216

Abstract

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

How to cite

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Benaouda, M., and Telega, J.. "Two-dimensional examples of rank-one convex functions that are not quasiconvex." Annales Polonici Mathematici 73.3 (2000): 291-295. <http://eudml.org/doc/262616>.

@article{Benaouda2000,
abstract = {The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.},
author = {Benaouda, M., Telega, J.},
journal = {Annales Polonici Mathematici},
keywords = {rank-one convex function; quasiconvexity; integral functional; weak lower semicontinuity},
language = {eng},
number = {3},
pages = {291-295},
title = {Two-dimensional examples of rank-one convex functions that are not quasiconvex},
url = {http://eudml.org/doc/262616},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Benaouda, M.
AU - Telega, J.
TI - Two-dimensional examples of rank-one convex functions that are not quasiconvex
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 3
SP - 291
EP - 295
AB - The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.
LA - eng
KW - rank-one convex function; quasiconvexity; integral functional; weak lower semicontinuity
UR - http://eudml.org/doc/262616
ER -

References

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  1. [1] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. Zbl0565.49010
  2. [2] J. M. Ball and F. Murat, W 1 , p -quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225-253. Zbl0549.46019
  3. [3] P. G. Ciarlet, Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity, North-Holland, Amsterdam, 1988. Zbl0648.73014
  4. [4] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, Berlin, 1989. Zbl0703.49001
  5. [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. Zbl0898.49012
  6. [6] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. 
  7. [7] P. Pedregal, Parametrized Measures and Variational Principles, Birkhäuser, Basel, 1997. 
  8. [8] V. Šverák, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), 185-189. Zbl0777.49015

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