Free access
Issue
ESAIM: COCV
Volume 17, Number 2, April-June 2011
Page(s) 472 - 492
DOI http://dx.doi.org/10.1051/cocv/2010016
Published online 23 April 2010
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Anal. 86 (1984) 125–145. [CrossRef] [MathSciNet]
  2. E. Acerbi and N. Fusco, A regularity theorem for minimizers of quasiconvex integrals. Arch. Ration. Mech. Anal. 99 (1987) 261–281.
  3. E. Acerbi and N. Fusco, Regularity for minimizers of non-quadratic functionals: the case 1<p<2. J. Math. Anal. Appl. 140 (1989) 115–135. [CrossRef] [MathSciNet]
  4. E. Acerbi and N. Fusco, Partial regularity under anisotropic (p, q) growth conditions. J. Differ. Equ. 107 (1994) 46–67. [CrossRef]
  5. E. Acerbi and G. Mingione, Regularity results for a class of quasiconvex functionals with nonstandard growth. Ann. Scuola Norm. Sup. Pisa Cl. Sci. IV 30 (2001) 311–339.
  6. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [CrossRef] [MathSciNet]
  7. M. Bildhauer and M. Fuchs, Partial regularity for variational integrals with (s, µ, q)-growth. Calc. Var. Partial Differ. Equ. 13 (2001) 537–560. [CrossRef]
  8. M. Bildhauer and M. Fuchs, C1, α-solutions to non-autonomous anisotropic variational problems. Calc. Var. Partial Differ. Equ. 24 (2005) 309–340. [CrossRef]
  9. G. Bouchitté, I. Fonseca and J. Malý, The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent. Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 463–479. [CrossRef] [MathSciNet]
  10. M. Carozza and A. Passarelli di Napoli, Partial regularity for anisotropic functionals of higher order. ESAIM: COCV 13 (2007) 692–706. [CrossRef] [EDP Sciences]
  11. M. Carozza, N. Fusco and G. Mingione, Partial regularity of minimizers of quasiconvex integrals with subquadratic growth. Ann. Mat. Pura Appl. IV 175 (1998) 141–164. [CrossRef] [MathSciNet]
  12. G. Cupini, M. Guidorzi and E. Mascolo, Regularity of minimizers of vectorial integrals with p-q growth. Nonlinear Anal., Theory Methods Appl. 54 (2003) 591–616.
  13. F. Duzaar and M. Kronz, Regularity of ω-minimizers of quasi-convex variational integrals with polynomial growth. Differ. Geom. Appl. 17 (2002) 139–152. [CrossRef]
  14. F. Duzaar and K. Steffen, Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals. J. Reine Angew. Math. 546 (2002) 73–138. [CrossRef] [MathSciNet]
  15. F. Duzaar, A. Gastel and J. Grotowski, Partial regularity for almost minimizers of quasi-convex integrals. SIAM J. Math. Anal. 32 (2000) 665–687. [CrossRef] [MathSciNet]
  16. F. Duzaar, J. Grotowski and M. Kronz, Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth. Ann. Mat. Pura Appl. IV 184 (2005) 421–448. [CrossRef] [MathSciNet]
  17. L. Esposito and G. Mingione, Relaxation results for higher order integrals below the natural growth exponent. Differ. Integral Equ. 15 (2002) 671–696.
  18. L. Esposito, F. Leonetti and G. Mingione, Regularity results for minimizers of irregular integrals with (p, q) growth. Forum Math. 14 (2002) 245–272. [CrossRef] [MathSciNet]
  19. L. Esposito, F. Leonetti and G. Mingione, Sharp regularity for functionals with (p, q) growth. J. Differ. Equ. 204 (2004) 5–55.
  20. L.C. Evans, Quasiconvexity and partial regularity in the calculus of variations. Arch. Ration. Mech. Anal. 95 (1986) 227–252.
  21. I. Fonseca and J. Malý, Relaxation of multiple integrals below the growth exponent. Ann. Inst. Henri Poincaré Anal. Non Linéaire 14 (1997) 309–338. [CrossRef] [MathSciNet]
  22. I. Fonseca and J. Malý, From jacobian to hessian: distributional form and relaxation. Riv. Mat. Univ. Parma 4 (2005) 45–74. [MathSciNet]
  23. N. Fusco and J. Hutchinson, C1, α partial regularity of functions minimising quasiconvex integrals. Manuscr. Math. 54 (1984) 121–143. [CrossRef] [MathSciNet]
  24. M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton University Press, Princeton (1983).
  25. M. Giaquinta, Growth conditions and regularity, a counterexample. Manuscr. Math. 59 (1987) 245–248. [CrossRef]
  26. M. Giaquinta and G. Modica, Partial regularity of minimizers of quasiconvex integrals. Ann. Inst. Henri Poincaré Anal. Non Linéaire 3 (1986) 185–208.
  27. M. Guidorzi, A remark on partial regularity of minimizers of quasiconvex integrals of higher order. Rend. Ist. Mat. Univ. Trieste 32 (2000) 1–24.
  28. M. Guidorzi and L. Poggiolini, Lower semicontinuity of quasiconvex integrals of higher order. NoDEA 6 (1999) 227–246. [CrossRef] [MathSciNet]
  29. M.C. Hong, Some remarks on the minimizers of variational integrals with non standard growth conditions. Boll. Un. Mat. Ital. A 6 (1992) 91–101. [MathSciNet]
  30. J. Kristensen, Lower semicontinuity in Sobolev spaces below the growth exponent of the integrand. Proc. Roy. Soc. Edinburgh Sect. A 127 (1997) 797–817. [MathSciNet]
  31. J. Kristensen and G. Mingione, The singular set of lipschitzian minima of multiple integrals. Arch. Ration. Mech. Anal. 184 (2007) 341–369. [CrossRef] [MathSciNet]
  32. M. Kronz, Partial regularity results for minimizers of quasiconvex functionals of higher order. Ann. Inst. Henri Poincaré Anal. Non Linéaire 19 (2002) 81–112. [CrossRef] [MathSciNet]
  33. P. Marcellini, Approximation of quasiconvex functions and lower semicontinuity of multiple integrals. Manuscr. Math. 51 (1985) 1–28. [CrossRef] [MathSciNet]
  34. P. Marcellini, On the definition and the lower semicontinuity of certain quasiconvex integrals. Ann. Inst. Henri Poincaré Anal. Non Linéaire 3 (1986) 391–409.
  35. P. Marcellini, Un exemple de solution discontinue d'un problème variationnel dans le cas scalaire. Preprint Istituto Matematico U. Dini, Universita' di Firenze (1987/1988), n. 11.
  36. P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions. Arch. Ration. Mech. Anal. 105 (1989) 267–284.
  37. P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions. J. Differ. Equ. 90 (1991) 1–30. [CrossRef] [MathSciNet]
  38. P. Marcellini, Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Sup. Pisa Cl. Sci. IV 23 (1996) 1–25.
  39. N.G. Meyers, Quasi-convexity and lower semi-continuity of multiple variational integrals of any order. Trans. Am. Math. Soc. 119 (1965) 125–149. [CrossRef] [MathSciNet]
  40. C.B. Morrey, Quasi-convexity and the lower semicontinuity of multiple integrals. Pac. J. Math. 2 (1952) 25–53.
  41. A. Passarelli di Napoli and F. Siepe, A regularity result for a class of anisotropic systems. Rend. Ist. Mat. Univ. Trieste 28 (1996) 13–31.
  42. S. Schemm and T. Schmidt, Partial regularity of strong local minimizers of quasiconvex integrals with (p, q)-growth. Proc. Roy. Soc. Edinburgh Sect. A 139 (2009) 595–621. [CrossRef] [MathSciNet]
  43. T. Schmidt, Regularity of minimizers of W1,p-quasiconvex variational integrals with (p, q)-growth. Calc. Var. Partial Differ. Equ. 32 (2008) 1–24. [CrossRef]
  44. T. Schmidt, Regularity of relaxed minimizers of quasiconvex variational integrals with (p, q)-growth. Arch. Ration. Mech. Anal. 193 (2009) 311–337. [CrossRef] [MathSciNet]
  45. F. Siepe and M. Guidorzi, Partial regularity for quasiconvex integrals of any order. Ric. Mat. 52 (2003) 31–54.