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ESAIM: COCV
Volume 13, Number 4, October-December 2007
Page(s) 639 - 656
DOI http://dx.doi.org/10.1051/cocv:2007039
Published online 05 September 2007
  1. E. Acerbi and N. Fusco, A regularity theorem for minimizers of quasiconvex integrals. Arch. Ration. Mech. Anal. 99 (1987) 261–281.
  2. F. Duzaar, A. Gastel and J.F. Grotowski, Partial regularity for almost minimizers of quasi-convex integrals. SIAM J. Math. Anal. 32 (2000) 665–687. [CrossRef] [MathSciNet]
  3. L.C. Evans, Quasiconvexity and partial regularity in the calculus of variations. Arch. Ration. Mech. Anal. 95 (1986) 227–252.
  4. L.C. Evans and R.F. Gariepy, Blowup, compactness and partial regularity in the calculus of variations. Indiana Univ. Math. J. 36 (1987) 361–371. [CrossRef] [MathSciNet]
  5. N. Fusco and J. Hutchinson, Formula partial regularity of functions minimising quasiconvex integrals. Manuscr. Math. 54 (1985) 121–143. [CrossRef] [MathSciNet]
  6. M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton Univ. Press, Princeton (1983).
  7. M. Giaquinta, The problem of the regularity of minimizers. Proc. Int. Congr. Math., Berkeley 1986 (1987) 1072–1083.
  8. M. Giaquinta, Quasiconvexity, growth conditions and partial regularity. Partial differential equations and calculus of variations, Lect. Notes Math. 1357 (1988) 211–237.
  9. M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals. Acta Math. 148 (1982) 31–46. [CrossRef] [MathSciNet]
  10. M. Giaquinta and E. Giusti, Differentiability of minima of non-differentiable functionals. Invent. Math. 72 (1983) 285–298. [CrossRef] [MathSciNet]
  11. M. Giaquinta and E. Giusti, Sharp estimates for the derivatives of local minima of variational integrals. Boll. Unione Mat. Ital. 3A (1984) 239–248.
  12. M. Giaquinta and P.-A. Ivert, Partial regularity for minima of variational integrals. Ark. Mat. 25 (1987) 221–229. [CrossRef] [MathSciNet]
  13. M. Giaquinta and G. Modica, Partial regularity of minimizers of quasiconvex integrals. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 3 (1986) 185–208.
  14. E. Giusti, Metodi diretti nel calcolo delle variazioni. UMI, Bologna (1994).
  15. C. Hamburger, Partial regularity for minimizers of variational integrals with discontinuous integrands. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 13 (1996) 255–282.
  16. C. Hamburger, A new partial regularity proof for solutions of nonlinear elliptic systems. Manuscr. Math. 95 (1998) 11–31. [CrossRef]
  17. C. Hamburger, Partial regularity of minimizers of polyconvex variational integrals. Calc. Var. 18 (2003) 221–241. [CrossRef] [MathSciNet]
  18. C. Hamburger, Partial regularity of solutions of nonlinear quasimonotone systems. Hokkaido Math. J. 32 (2003) 291–316. [MathSciNet]
  19. C. Hamburger, Partial boundary regularity of solutions of nonlinear superelliptic systems. Boll. Unione Mat. Ital. 10B (2007) 63–81.
  20. M.-C. Hong, Existence and partial regularity in the calculus of variations. Ann. Mat. Pura Appl. 149 (1987) 311–328. [CrossRef] [MathSciNet]
  21. J. Kristensen and G. Mingione, The singular set of Formula -minima. Arch. Ration. Mech. Anal. 177 (2005) 93–114. [CrossRef] [MathSciNet]
  22. J. Kristensen and G. Mingione, The singular set of minima of integral functionals. Arch. Ration. Mech. Anal. 180 (2006) 331–398. [CrossRef] [MathSciNet]
  23. J. Kristensen and G. Mingione, The singular set of Lipschitzian minima of multiple integrals. Arch. Ration. Mech. Anal. 184 (2007) 341–369. [CrossRef] [MathSciNet]
  24. D. Phillips, A minimization problem and the regularity of solutions in the presence of a free boundary. Indiana Univ. Math. J. 32 (1983) 1–17. [CrossRef] [MathSciNet]