Free access
Issue
ESAIM: COCV
Volume 14, Number 3, July-September 2008
Page(s) 456 - 477
DOI http://dx.doi.org/10.1051/cocv:2007061
Published online 21 November 2007
  1. M. Amar, and G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients. Ann. Inst. Henri Poincaré 11 (1994) 91–133.
  2. M. Amar and V. De Cicco, Relaxation in BV for a class of functionals without continuity assumptions. NoDEA Nonlinear Differential Equations Appl. (to appear).
  3. M. Amar, V. De Cicco and N. Fusco, A relaxation result in BV for integral functionals with discontinuous integrands. ESAIM: COCV 13 (2007) 396–412. [CrossRef] [EDP Sciences]
  4. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford University Press, New York (2000).
  5. G. Anzellotti, G. Buttazzo and G. Dal Maso, Dirichlet problem for demi-coercive functionals. Nonlinear Anal. 10 (1986) 603–613. [CrossRef] [MathSciNet]
  6. G. Bouchitté and M. Valadier, Integral representation of convex functionals on a space of measures. J. Funct. Anal. 80 (1988) 398–420. [CrossRef] [MathSciNet]
  7. G. Bouchitté, I. Fonseca and L. Mascarenhas, A global method for relaxation. Arch. Rat. Mech. Anal. 145 (1998) 51–98. [CrossRef]
  8. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation Problems in the Calculus of Variations. Pitman Res. Notes in Math., Longman, Harlow (1989).
  9. M. Carriero, G. Dal Maso, A. Leaci and E. Pascali, Relaxation of the non-parametric Plateau problem with an obstacle. J. Math. Pures Appl. 67 (1988) 359–396. [MathSciNet]
  10. G. Dal Maso, Integral representation on Formula of Γ-limits of variational integrals. Manuscripta Math. 30 (1980) 387–416. [CrossRef]
  11. G. Dal Maso, On the integral representation of certain local functionals. Ricerche di Matematica 32 (1983) 85–113. [MathSciNet]
  12. G. Dal Maso, An Introduction to Γ-convergence. Birkhäuser, Boston (1993).
  13. V. De Cicco and G. Leoni, A chain rule in Formula and its applications to lower semicontinuity. Calc. Var. Partial Differential Equations 19 (2004) 23–51.
  14. V. De Cicco, N. Fusco and A. Verde, On L1-lower semicontinuity in Formula . J. Convex Analysis 12 (2005) 173–185.
  15. V. De Cicco, N. Fusco and A. Verde, A chain rule formula in Formula and its applications to lower semicontinuity. Calc. Var. Partial Differential Equations 28 (2007) 427–447. [CrossRef]
  16. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975) 842–850. [MathSciNet]
  17. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Rend. Sem. Mat. Brescia 3 (1979) 63–101.
  18. H. Federer and W.P. Ziemer, The Lebesgue set of a function whose distribution derivatives are p-th power summable. Indiana Un. Math. J. 22 (1972) 139–158. [CrossRef] [MathSciNet]
  19. I. Fonseca and G. Leoni, On lower semicontinuity and relaxation. Proc. Royal Soc. Edinb., Sect. A, Math. 131 (2001) 519–565.
  20. I. Fonseca and S. Müller, Quasi-convex integrands and lower semicontinuity in L1. SIAM J. Math. Anal. 23 (1992) 1081–1098. [CrossRef] [MathSciNet]
  21. I. Fonseca and S. Müller, Relaxation of quasiconvex functionals in BVFormula for integrands Formula . Arch. Rat. Mech. Anal. 123 (1993) 1–49. [CrossRef] [MathSciNet]
  22. N. Fusco, F. Giannetti and A. Verde, A remark on the L1-lower semicontinuity for integral functionals in BV. Manuscripta Math. 112 (2003) 313–323. [CrossRef] [MathSciNet]
  23. N. Fusco, M. Gori and F. Maggi, A remark on Serrin's Theorem. NoDEA Nonlinear Differential Equations Appl. 13 (2006) 425–433. [CrossRef] [MathSciNet]
  24. M. Gori and F. Maggi, The common root of the geometric conditions in Serrin's semicontinuity theorem. Ann. Mat. Pura Appl. 184 (2005) 95–114. [CrossRef] [MathSciNet]
  25. M. Gori, F. Maggi and P. Marcellini, On some sharp conditions for lower semicontinuity in L1. Diff. Int. Eq. 16 (2003) 51–76.
  26. F. Maggi, On the relaxation on BV of certain non coercive integral functionals. J. Convex Anal. 10 (2003) 477–489. [MathSciNet]
  27. M. Miranda, Superfici cartesiane generalizzate ed insiemi di perimetro localmente finito sui prodotti cartesiani. Ann. Scuola Norm. Sup. Pisa 18 (1964) 515–542. [MathSciNet]
  28. Y.G. Reshetnyak, Weak convergence of completely additive vector functions on a set. Siberian Math. J. 9 (1968) 1039–1045.