A singular minimizer of a smooth strongly convex functional in three dimensions

Calculus of Variations and Partial Differential Equations

Volumn 10, Issue 3, 2000, Pages 213-221

  Šverák, Vladimír ^a   Yan, Xiaodong ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037510797     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050151     Document Type: Article

References (18)

1. J. M. Ball: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1978), 337-403.
2. 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.
3. Theodor Bröcker, Tammo tom Dieck: Representations of Compact Lie Groups, Springer-Verlag, New York, 1985
4. B. Dacorogna: Direct methods in the Calculus of Variations, Springer-Verlag, 1989.
5. E. De Giorgi: Sulla differenziabilità e l'analitità della estremali degli integrali multipi regolari, Mem. Accad. Sci. Torino cl. Sci. Fis. Mat. Nat.(3) 3 (1957), 25-43.
6. E. De Giorgi: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. UMI 4 (1968), 135-137.
7. M. Giaquinta: Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton University Press, Princeton, 1983.
8. E. Giusti, M. Miranda: Un esempio di soluzione discontinua per un problem di minimo relativo ad un integrale regolare del calcolo delle varazioni, Boll. Un. Mat. Ital. 2 (1968), 1-8.
9. Morris W. Hirsch: Differential Topology. New York, Springer Verlag, 1976.
10. W. Hao, S. Leonardi, J. Nečas: An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), no. 1, 57-67.
11. A. I. Koshelev: Regularity problem for quasilinear elliptic and parabolic systems, Springer, 1995.
12. C. B. Morrey: Multiple integrals in the calculus of variations. Springer Verlag, Heidelberg, New York, (1966).
13. J. Nash: Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 8 (1958), 931-954.
14. J. Nečas: Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions of regularity, Theory of Non Linear Operators, Abhandlungen Akad, der Wissen. der DDR(1977), Proc. of a Summer School held in Berlin (1975).
15. J. Nečas, O. John, J. Stará: Counterexample to the regularity of weak solutions of elliptic systems. Comment. Math. Univ. Carolinae 21 (1980), 145-154.
16. Tyrrell R. Rockafellar: Convex analysis. Princeton, N.J. Princeton University Press, 1970.
17. H. Weyl: The Classical Groups. Their Invariants and Representations. Princeton, New Jersey. 1939
18. H. Weyl: On the volume of tubes. American Journal of Mathematics, 61 (1939) 461-472.