Finding new families of rank-one convex polynomials

Luís Bandeira; Pablo Pedregal

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1621-1634
  • ISSN: 0294-1449

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Bandeira, Luís, and Pedregal, Pablo. "Finding new families of rank-one convex polynomials." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1621-1634. <http://eudml.org/doc/78906>.

@article{Bandeira2009,
author = {Bandeira, Luís, Pedregal, Pablo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {rank-one convexity; laminate},
language = {eng},
number = {5},
pages = {1621-1634},
publisher = {Elsevier},
title = {Finding new families of rank-one convex polynomials},
url = {http://eudml.org/doc/78906},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Bandeira, Luís
AU - Pedregal, Pablo
TI - Finding new families of rank-one convex polynomials
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 5
SP - 1621
EP - 1634
LA - eng
KW - rank-one convexity; laminate
UR - http://eudml.org/doc/78906
ER -

References

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  1. [1] Alibert J.J., Dacorogna B., An example of a quasiconvex function not polyconvex in dimension 2, Arch. Rational Mech. Anal.117 (1992) 155-166. Zbl0761.26009MR1145109
  2. [2] Ball J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal.63 (1977) 337-403. Zbl0368.73040MR475169
  3. [3] Dacorogna B., Direct Methods in the Calculus of Variations, Springer, 1989. Zbl0703.49001MR990890
  4. [4] Dacorogna B., Douchet J., Gangbo W., Rappaz J., Some examples of rank one convex functions in dimension two, Proc. Roy. Soc. Edinburgh Sect. A114 (1–2) (1990) 135-150. Zbl0722.49018MR1051612
  5. [5] Dacorogna B., Marcellini P., A counterexample in the vectorial calculus of variations, in: Material Instabilities in Continuum Mechanics, Oxford Sci. Publ., Oxford Univ. Press, New York, 1988, pp. 77-83. Zbl0641.49007MR970519
  6. [6] Gutiérrez S., A necessary condition for the quasiconvexity of polynomials of degree four, J. Convex Anal.13 (1) (2006) 51-60. Zbl1115.49016MR2211803
  7. [7] Morrey C.B., Quasiconvexity and the lower semicontinuity of multiple integrals, Pacific J. Math.2 (1952) 25-53. Zbl0046.10803MR54865
  8. [8] Pedregal P., Laminates and microstructure, Eur. J. Appl. Math.4 (2) (1993) 121-149. Zbl0779.73050MR1228114
  9. [9] Schost E., Computing parametric geometric resolutions, Appl. Algebra Engrg. Comm. Comput.13 (5) (2003) 349-393. Zbl1058.68123MR1959170
  10. [10] Wang D., Elimination Methods, Texts and Monographs in Symbolic Computation, Springer, 2001. Zbl0964.13014MR1826878
  11. [11] Weispfenning V., Comprehensive Gröbner bases, J. Symbolic Comput.14 (1992) 1-29. Zbl0784.13013MR1177987

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