The Regularity of Critical Points of Polyconvex Functionals

Archive for Rational Mechanics and Analysis

Volumn 171, Issue 5, 2004, Pages 133-152

  Székelyhidi Jr , László ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142719779     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-003-0300-7     Document Type: Article

References (22)

1. [AH86] AUMANN, R.J., HART, S.: Bi-convexity and bi-martingales. Israel J. Math. 54, 159-180 (1986)
2. [Bal77] BALL, J.M.: Constitutive inequalities and existence theorems in nonlinear elastostatics. In: Nonlinear analysis and mechanics: Heriot-Watt Symposium (Edinburgh 1976) Vol. I. Res. Notes in Math., No. 17. Pitman, London, 1977, pp. 187-241
3. [Bal80] BALL, J.M.: Strict convexity, strong ellipticity and regularity in the calculus of variations. Math. Proc. Cambridge Philos. Soc. 87, 501-513 (1980)
4. [BJ87] BALL, J.M., JAMES, R.D.: Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100, 13-52 (1987)
5. [CK88] CHIPOT, M., KINDERLEHRER, D.: Equilibrium configurations of crystals. Arch. Rational Mech. Anal. 103, 237-277 (1988)
6. [CT93] CASADIO TARABUSI, E.: An algebraic characterization of quasi-convex functions. Ricerche Mat. 42, 11-24 (1993)
7. [Eva86] EVANS, L.C.: Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95, 227-252 (1986)
8. [GP74] GUILLEMIN, V., POLLACK, A.: Differential topology. Prentice-Hall Inc., Englewood Cliffs, NJ, 1974
9. [Gro86] GROMOV, M.: Partial differential relations, volume 9 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) Springer-Verlag, Berlin, 1986
10. [Kir03] KIRCHHEIM, B.: Rigidity and Geometry of microstructures. Habilitation thesis, University of Leipzig, 2003
11. [KMŠ03] KIRCHHEIM, B., MÜLLER, S., ŠVERÁK, V.: Studying nonlinear PDE by geometry in matrix space. In: Gemetric analysis and Nonlinear partial differential equations, STEFAN HILDEBRANDT & HERMANN KARCHER, (eds.), Springer-Verlag, 2003, pp. 347-395
12. [KT01] KRISTENSEN, J., TAHERI, A.: Partial regularity of strong local minimizers in the multi-dimensional calculus of variations. Arch. Rational Mech. Anal. 170, 63-89 (2003)
13. 1-isometric imbeddings. Nederl. Akad. Wetensch. Proc. Ser. A 58, 545-556 (1955)
14. [Mor66] MORREY, Jr. C.B.: Multiple integrals in the calculus of variations. Die Grundlehren der mathematischen Wissenschaften, Band 130. Springer-Verlag New York, Inc., New York, 1966
15. [MŠ03] MÜLLER, S., ŠVERÁK, V.: Convex integration for Lipschitz mappings and counterexamples to regularity. Ann. Math. (2) 157, 715-742 (2003)
16. 1 isometric imbeddings. Ann. Math. (2) 60, 383-396 (1954)
17. [NM91] NESI, V., MILTON G.W.: Polycrystalline configurations that maximize electrical resistivity. J. Mech. Phys. Solids 39, 525-542 (1991)
18. [Ped93] PEDREGAL, P.: Laminates and microstructure. Eur. J. Appl. Math. 4, 121-149 (1993)
19. [Sch74] SCHEFFER, V.: Regularity and irregularity of solutions to nonlinear second order elliptic systems and inequalities. Dissertation, Princeton University, 1974
20. [Šve95] ŠVERÁK, V.: Lower-semicontinuity of variational integrals and compensated compactness. In: Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zurich 1994), Birkhäuser, Basel, 1995, pp. 1153-1158
21. [Tar79] TARTAR, L.: Compensated compactness and applications to partial differential equations. In: Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, volume 39 of Res. Notes in Math. Pitman, Boston, Mass., 1979, pp. 136-212
22. [Tar93] TARTAR, L.: Some remarks on separately convex functions. In Microstructure and phase transition, volume 54 of IMA Vol. Math. Appl. Springer, New York, 1993, pp. 191-204