Polyconvex functionals for nearly conformal deformations

SIAM Journal on Mathematical Analysis

Volumn 27, Issue 3, 1996, Pages 609-619

  Iwaniec, Tadeusz ^a   Lutoborski, Adam ^a  

^a SYRACUSE UNIVERSITY   (United States)

Author keywords

Mean coercive functionals; Nearly conformal deformations; Polyconvex functions

Indexed keywords

EID: 0030541949     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/0527033     Document Type: Article

References (17)

1. J.-J. ALIBERT AND B. DACOROGNA, An example of a quasiconvex function that is not polyconvex in two dimensions, Arch. Rational Mech. Anal., 117 (1992), pp. 155-166.
2. G. AUBBRT, On a counterexample of a rank 1 convex function which is not polyconvex in the case N = 2, Proc. Roy. Soc. Edinburgh Sect A, 106 (1987), pp. 237-240.
3. J. M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 63 (1977), pp. 337-403.
4. B. BOJARSKI AND T. IWANIEC, Another approach to Liouville theorem, Math. Nachr., 107 (1982), pp. 253-262.
5. B. DACOROGNA, Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, New York, 1989.
6. B. DACOROGNA, J. DOUCHET, W. GANGBO, AND J. RAPPAZ, Some examples of rank one convex functions in dimension two, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), pp. 135-150.
7. B. DACOROGNA AND H. KOSHIGOE, On the different notions of convexity for rotationally invariant functions, Ann. Fac. Sci. Toulouse Math., II (1993), pp. 163-184.
8. B. DACOROGNA AND P. MARCELLINI, A counterexample in the vectorial calculus of variations, in Material Instabilities in Continuum Mechanics, J. M. Ball, ed., Oxford University Press, Oxford, 1988, pp. 77-83.
9. N. DUNFORD AND J. T. SCHWARTZ, Linear Operators, Part 1, Interscience, New York, 1967.
10. T. IWANIEC AND A. LUTOBORSKI, Integral estimates for null Lagrangians, Arch. Rational Mech. Anal., 125 (1993), pp. 25-79.
11. T. IWANIEC AND G. MARTIN, Quasiregular mappings in even dimensions, Acta Math., 170 (1993), pp. 29-81.
12. F. W. GEHRING, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc., 103 (1962), pp. 353-393.
13. Y. G. RESHETNYAK, Liouville's conformal mapping theorem under minimal regularity assumption, Siberian Math. J., 8 (1967), pp. 835-840.
14. _, Stability theorems for mappings with bounded distortion, Siberian Math. J., 8 (1968), pp. 499-512.
15. P. ROSAKIS AND H. C. SIMPSON, On the relation between polyconvexity and rank-one convexity in nonlinear elasticity, J. Elasticity, 37 (1995), pp. 113-137.
16. V. ŠVERÁK, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh Sect. A, 120 (1992), pp. 185-189.
17. _, Quasiconvex functions with subquadratic growth, Proc. Roy. Soc. London, 433 (1991), pp. 723-725.