On directional convexity

Discrete and Computational Geometry

Volumn 25, Issue 3, 2001, Pages 389-403

  Matousek J ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038974645     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004540010069     Document Type: Article

References (16)

1. R. Aumann and S. Hart. Bi-convexity and bi-martingales. Israel. J. Math., 54(2):159-180, 1986.
2. K. Bhattacharya, N. B. Firoozye, R. D. James, and R. V. Kohn. Restrictions on microstructure. Proc. Roy. Soc. Edinburgh Sect. A, 124:843-878, 1994.
3. E. Casadio-Tarabusi. An algebraic characterization of quasiconvex functions. Ricerche Mat., 42:11-24, 1993.
4. G. Dolzmann, B. Kirchheim, S. Müller, and V. Šverák. The two-well problem in three dimensions. Calc. Var. Partial Differential Equations, 10(1):21-40, 2000.
5. B. Kirchheim. On the geometry of rank-one convex hulls. Manuscript, Max Planck Institute for Mathematics in the Sciences, Leipzig, 1999.
6. B. Kirchheim, J. Kristensen, and J. Ball. Regularity of quasiconvex envelopes. Preprint 72/1999, Max Planck Institute for Mathematics in the Sciences, Leipzig, 1999.
7. B. Letocha. Directional convexity (in Czech). M.Sc. Thesis, Department of Applied Mathematics, Charles University, Prague, 1999.
8. C. B. Morrey. Quasi-convexity and the lower semicontinuity of multiple integrals. Pacific J. Math., 2:25-53, 1952.
9. J. Matoušek and P. Plecháč. On functional separately convex hulls. Discrete Comput. Geom., 19:105-130, 1998.
10. S. Müller and V. Šverák. Convex integration for Lipschitz mappings and counterexamples to regularity. Preprint 26/1999, Max Planck Institute for Mathematics in the Sciences, Leipzig, 1999.
11. S. Müller and V. Šverák. Convex integration with constraints and applications to phase transitions and partial differential equations. J. European Math. Soc., 1(4):393-422, 1999.
12. S. Müller. Variational models for microstructure and phase transitions. In Calculus of Variations and Geometric Evolution Problems (S. Hildebrandt et al., eds.), pages 85-210. Lecture Notes in Mathematics, vol. 1713. Springer-Verlag, Berlin, 1999.
13. S. Müller. Rank-one convexity implies quasiconvexity on diagonal matrices. Internat. Math. Res. Not. 1999, 20:1087-1095, 1999.
14. V. Scheffer. Regularity and irregularity of solutions to nonlinear second order elliptic systems of partial differential equations and inequalities. Dissertation, Princeton University, 1974.
15. V. Šverák. New examples of quasiconvex functions. Proc. Roy. Soc. Edinburgh Sect. A, 120:185-189, 1992.
16. L. Tartar. On separately convex functions. In Microstructure and Phase Transition, The IMA Volumes in Mathematics and Its Applications, vol. 54 (D. Kinderlehrer et al., eds.), pages 191-204. Springer-Verlag, Berlin, 1993.