On quasiconvex hulls in symmetric 2 × 2 matrices

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 23, Issue 6, 2006, Pages 865-876

  Székelyhidi Jr , László ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Gradient Young measure; Maximum principle; Quasiconvex hull

Indexed keywords

COMPUTATIONAL GEOMETRY; MAXIMUM LIKELIHOOD ESTIMATION;

GRADIENT YOUNG MEASURE; QUASICONVEX HULL;

MATRIX ALGEBRA;

EID: 33750177411     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2005.11.001     Document Type: Article

References (23)

1. Astala K., and Faraco D. Quasiregular mappings and Young measures. Proc. Roy. Soc. Edinburgh Sect. A 132 5 (2002) 1045-1056
2. K. Astala, T. Iwaniec, G. Martin, Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane, J. Reine Angew. Math., in press
3. Ball J.M. A version of the fundamental theorem for Young measures. PDEs and Continuum Models of Phase Transitions (Nice, 1988). Lecture Notes in Phys. vol. 344 (1989), Springer, Berlin 207-215
4. J.M. Ball, R.D. James, Incompatible sets of gradients and metastability, in preparation
5. Ball J.M., and James R.D. Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100 (1987) 13-52
6. B. Bojarski, L. D'Onofrio, T. Iwaniec, C. Sbordone, G-closed classes of elliptic operators in the complex plane, in press
7. Caffarelli L.A., and Cabré X. Fully Nonlinear Elliptic Equations. Amer. Math. Soc. Colloq. Publ. vol. 43 (1995), American Mathematical Society, Providence, RI
8. 2 × 2. C. R. Acad. Sci. Paris Sér. I Math. 331 11 (2000) 851-856
9. Chipot M., and Kinderlehrer D. Equilibrium configurations of crystals. Arch. Rational Mech. Anal. 103 (1988) 237-277
10. 2 × 2. C. R. Math. Acad. Sci. Paris, Ser. I 337 4 (2003) 233-238
11. Dacorogna B., and Tanteri C. Implicit partial differential equations and the constraints of nonlinear elasticity. J. Math. Pures Appl. (9) 81 4 (2002) 311-341
12. Dolzmann G. Variational Methods for Crystalline Microstructure - Analysis and Computation. Lecture Notes in Math. vol. 1803 (2003), Springer-Verlag, Berlin
13. Faraco D., and Zhong X. Quasiconvex functions and Hessian equations. Arch. Rational Mech. Anal. 168 3 (2003) 245-252
14. Gilbarg D., and Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Classics Math. (2001), Springer-Verlag, Berlin (Reprint of the 1998 edition)
15. Kinderlehrer D., and Pedregal P. Characterizations of Young measures generated by gradients. Arch. Rational Mech. Anal. 115 (1991) 329-365
16. Matos J.P. Young measures and the absence of fine microstructures in a class of phase transitions. Eur. J. Appl. Math. 3 1 (1992) 31-54
17. Müller S. Rank-one convexity implies quasiconvexity on diagonal matrices. Int. Math. Res. Notices 20 (1999) 1087-1095
18. Müller S. Variational models for microstructure and phase transitions. Calculus of Variations and Geometric Evolution Problems (Cetraro, 1996). Lecture Notes in Math. vol. 1713 (1999), Springer, Berlin 85-210
19. V. Šverák, On regularity for the Monge-Ampère equations, Preprint, Heriot-Watt University, 1991
20. Šverák V. New examples of quasiconvex functions. Arch. Rational Mech. Anal. 119 4 (1992) 293-300
21. 2 × 2. Calc. Var. Partial Differential Equations 22 3 (2005) 253-281
22. Tartar L. Compensated compactness and applications to partial differential equations. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. IV. Res. Notes in Math. vol. 39 (1979), Pitman, Boston, MA 136-212
23. Zhang K. On separation of gradient Young measures. Calc. Var. Partial Differential Equations 17 1 (2003) 85-103