Free access
Issue
ESAIM: COCV
Volume 16, Number 4, October-December 2010
Page(s) 833 - 855
DOI http://dx.doi.org/10.1051/cocv/2009025
Published online 31 July 2009
  1. R. Alicandro and C. Leone, 3D-2D asymptotic analysis for micromagnetic energies. ESAIM: COCV 6 (2001) 489–498. [CrossRef] [EDP Sciences]
  2. L. Ambrosio and G. Dal Maso, On the relaxation in Formula of quasiconvex integrals. J. Funct. Anal. 109 (1992) 76–97.
  3. J.-F. Babadjian and V. Millot, Homogenization of variational problems in manifold valued Formula -spaces. Calc. Var. Part. Diff. Eq. 36 (2009) 7–47. [CrossRef]
  4. F. Béthuel, The approximation problem for Sobolev maps between two manifolds. Acta Math. 167 (1991) 153–206. [CrossRef] [MathSciNet]
  5. F. Béthuel and X. Zheng, Density of smooth functions between two manifolds in Sobolev spaces. J. Funct. Anal. 80 (1988) 60–75. [CrossRef] [MathSciNet]
  6. F. Béthuel, H. Brézis and J.M. Coron, Relaxed energies for harmonic maps, in Variational methods, Paris (1988), H. Berestycki, J.M. Coron and I. Ekeland Eds., Progress in Nonlinear Differential Equations and Their Applications 4, Birkhäuser, Boston (1990) 37–52.
  7. A. Braides, Homogenization of some almost periodic coercive functional. Rend. Accad. Naz. Sci. XL 103 (1985) 313–322.
  8. A. Braides and A. Defranceschi, Homogenization of multiple integrals, Oxford Lecture Series in Mathematics and its Applications 12. Oxford University Press, New York (1998).
  9. A. Braides, A. Defranceschi and E. Vitali, Homogenization of free discontinuity problems. Arch. Rational Mech. Anal. 135 (1996) 297–356. [CrossRef] [MathSciNet]
  10. H. Brézis, J.M. Coron and E.H. Lieb, Harmonic maps with defects. Comm. Math. Phys. 107 (1986) 649–705. [CrossRef] [MathSciNet]
  11. B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag (1989).
  12. B. Dacorogna, I. Fonseca, J. Malý and K. Trivisa, Manifold constrained variational problems. Calc. Var. Part. Diff. Eq. 9 (1999) 185–206. [CrossRef] [MathSciNet]
  13. G. Dal Maso, An Introdution to Γ-convergence. Birkhäuser, Boston (1993).
  14. I. Ekeland and R. Temam, Analyse convexe et problèmes variationnels. Dunod, Gauthiers-Villars, Paris (1974).
  15. I. Fonseca and S. Müller, Quasiconvex integrands and lower semicontinuity in L1. SIAM J. Math. Anal. 23 (1992) 1081–1098. [CrossRef] [MathSciNet]
  16. I. Fonseca and S. Müller, Relaxation of quasiconvex functionals in Formula for integrands Formula . Arch. Rational Mech. Anal. 123 (1993) 1–49.
  17. I. Fonseca, S. Müller and P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 (1998) 736–756. [CrossRef] [MathSciNet]
  18. M. Giaquinta, L. Modica and J. Souček, Cartesian currents in the calculus of variations, Modern surveys in Mathematics 37-38. Springer-Verlag, Berlin (1998).
  19. M. Giaquinta, L. Modica and D. Mucci, The relaxed Dirichlet energy of manifold constrained mappings. Adv. Calc. Var. 1 (2008) 1–51. [CrossRef] [MathSciNet]
  20. P. Marcellini, Periodic solutions and homogenization of nonlinear variational problems. Ann. Mat. Pura Appl. (4) 117 (1978) 139–152. [CrossRef] [MathSciNet]
  21. S. Müller, Homogenization of nonconvex integral functionals and cellular elastic materials. Arch. Rational Mech. Anal. 99 (1987) 189–212. [MathSciNet]