The failure of rank-one connections

Archive for Rational Mechanics and Analysis

Volumn 163, Issue 2, 2002, Pages 125-169

  Iwaniec, Tadeusz ^a   Verchota, Gregory C ^a   Vogel, Andrew L ^a  

^a SYRACUSE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035999221     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200197     Document Type: Article

References (31)

1. [AB50] L.V. AHLFORS & A. BEURLING, Conformal invariants and function theoretic null sets, Acta Math. 83 (1950), 101-129.
2. [Ant76] S.S. ANTMAN, Fundamental mathematical problems in the theory of nonlinear elasticity, North Holland, 1976.
3. [Bal77] J.M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403.
4. [Bal97] J. M. BALL, Nucleation in phase transformations of crystals, Lecture in Saariselkä, Finland, June 1997. Reporting joint work with C. CARSTENSEN.
5. [BC01] J.M. BALL & C. CARSTENSEN, Hadamard's compatibility condition for microstructures. In progress, 2001.
6. [BCO81] J.M. BALL, J. C. CURRIE & P.J. OLVER, Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Funct. Anal. 41 (1981), 135-174.
7. [BJ87] J.M. BALL & R. D. JAMES, Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 13-52.
8. [BK98] D. BURAGO & B. KLEINER, Separated nets in Euclidean space and Jacobians of bi-Lipschitz maps, Geom. Funct. Anal. 8 (1998), 273-282.
9. [Boj58] B. BOJARSKI, Some boundary value problems for systems of 2m equations of elliptic type in the plane, Dokl. Akad. Nauk. SSSR 124 (1958), 15-18, Russian.
10. [Boj66] B. BOJARSKI, Theory of generalized analytic vectors, Ann. Pol. Math. 17 (1966), 281-320, Russian.
11. [BW95] R. BAÑUELOS & G. WANG, Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. J. 80 (1995), 575-600.
12. [Cia87] P.B. CIARLET, Mathematical Elasticity, North Holland, Amsterdam, 1987.
13. [Dac89] B. DACOROGNA, Direct methods in the calculus of variations, Applied Mathematical Sciences, vol. 78, Springer-Verlag, 1989.
14. [DM90] B. DACOROGNA & J. MOSER, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré (1990), 1-26.
15. [Dou53] A. DOUGLIS, A function-theoretical approach to elliptic systems of equations in two variables, Comm. Pure Appl. Math. 6 (1953), 259-289.
16. [Ede62] D.G.B. EDELEN, The null set of the Euler-Lagrange operator, Arch. Rational Mech. Anal. 11 (1962), 117-121.
17. [Gro85] M. GROMOV, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
18. [IL93] T. IWANIEC & A. LUTOBORSKI, Integral estimates for null Lagrangians, Arch. Rational Mech. Anal. 125 (1993), 25-79.
19. [IM01] T. IWANIEC & B. MARTIN, Geometric function theory and nonlinear analysis, Oxford Mathematical Monographs, Clarendon Press, 2001.
20. [Kir02] B. KIRCHHEIM, Geometry and Rigidity of Microstructures, Habilitation Thesis, Leipzig, 2002. In progress.
21. [KP] B. KIRCHHEIM & D. PREISS, Construction of Lipschitz mappings having finitely many gradients without rank-one connections. In preparation.
22. [MCM98] C.T. MCMULLEN, Lipschitz maps and nets in Euclidean space, Geom. Funct. Anal. 8 (1998), 304-314.
23. [Mor38] C.B. MORREY, On the solutions of quasilinear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), 126-166.
24. [Mor52] C.B. MORREY, Quasiconvexity and the semicontinuity of multiple integrals, Pacific J. Math. 2 (1952), 25-53.
25. [Mos65] J. MOSER, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294.
26. [NV] F. NAZAROV & A. VOLBERG, Heating of the Beurling operator and the estimates of its norm, Amer. Journal of Math., to appear.
27. [Res89] Yu. G. RESHETNYAK, Space mappings with bounded distortion, Translations of Mathematical Monographs 73 (1989), AMS.
28. [RY96] T. RIVIÈRE & D. YE, Resolutions of the prescribed volume form equation, Nonlinear Differential Equations Appl. 3 (1996), 323-369.
29. [Šve91] V. ŠVERÁK, On regularity for the Monge-Ampère equations, preprint, 1991.
30. [Šve92] V. ŠVERÁK, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh 120 (1992), 185-189, Sec. A.
31. [Wen79] W.L. WENDLAND, Elliptic systems in the plane, Pitman, 1979.