Free access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 105 - 124
DOI http://dx.doi.org/10.1051/cocv:2003002
Published online 15 September 2003
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the Calculus of Variations. Arch. Rational Mech. Anal. 86 (1984) 125-145. [CrossRef] [MathSciNet]
  2. L. Ambrosio, Introduzione alla Teoria Geometrica della Misura e Applicazioni alle Superfici Minime, Lectures Notes. Scuola Normale Superiore, Pisa (1996).
  3. L. Ambrosio, On the lower-semicontinuity of quasi-convex integrals in SBV. Nonlinear Anal. 23 (1994) 405-425. [CrossRef] [MathSciNet]
  4. L. Ambrosio, G. Buttazzo and I. Fonseca, Lower-semicontinuity problems in Sobolev spaces with respect to a measure. J. Math. Pures Appl. 75 (1996) 211-224. [MathSciNet]
  5. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225-253. [CrossRef] [MathSciNet]
  6. G. Bouchitté and G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. 3 (2001) 139-168. [CrossRef] [MathSciNet]
  7. G. Bouchitté, G. Buttazzo and I. Fragalà, Mean curvature of a measure and related variational problems. Ann. Scuola Norm. Sup. Pisa. Cl. Sci. IV XXV (1997) 179-196.
  8. G. Bouchitté, G. Buttazzo and I. Fragalà, Convergence of Sobolev spaces on varying manifolds. J. Geom. Anal. 11 (2001) 399-422. [MathSciNet]
  9. G. Bouchitté, G. Buttazzo and P. Seppecher, Energies with respect to a measure and applications to low dimensional structures. Calc. Var. Partial Differential Equations 5 (1997) 37-54. [MathSciNet]
  10. G. Bouchitté and I. Fragalà, Homogenization of thin structures by two-scale method with respect to measures. SIAM J. Math. Anal. 32 (2001) 1198-1126. [CrossRef] [MathSciNet]
  11. G. Bouchitté and I. Fragalà, Homogenization of elastic thin structures: A measure-fattening approach. J. Convex. Anal. (to appear).
  12. A. Braides, Semicontinuity, Γ-convergence and Homogenization for Multiple Integrals, Lectures Notes. SISSA, Trieste (1994).
  13. G. Buttazzo, Semicontinuity, Relaxation, and Integral Representation in the Calculus of Variations. Longman, Harlow, Pitman Res. Notes Math. Ser. 207 (1989).
  14. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer-Verlag, Berlin, Appl. Math. Sci. 78 (1988).
  15. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Ann Harbor, Stud. in Adv. Math. (1992).
  16. H. Federer, Geometric Measure Theory. Springer-Verlag, Berlin (1969).
  17. I. Fonseca and S. Müller, Quasi-convex integrands and lower semicontinuity in L 1. SIAM J. Math. Anal. 23 (1992) 1081-1098. [CrossRef] [MathSciNet]
  18. I. Fragalà and C. Mantegazza, On some notions of tangent space to a measure. Proc. Roy. Soc. Edinburgh 129A (1999) 331-342.
  19. P. Hajlasz and P. Koskela, Sobolev met Poincaré. Mem. Amer. Math. Soc. 145 (2000).
  20. P. Hajlasz and P. Koskela, Sobolev meets Poincaré. C. R. Acad. Sci. Paris 320 (1995) 1211-1215.
  21. A.D. Ioffe, On lower semicontinuity of integral functionals I and II. SIAM J. Contol Optim. 15 (1997) 521-538 and 991-1000. [CrossRef]
  22. J. Kristensen, Lower semicontinuity in spaces of weakly differentiable functions. J. Math. Ann. 313 (1999) 653-710. [CrossRef] [MathSciNet]
  23. J. Maly, Lower semicontinuity of quasiconvex integrals. Manuscripta Math. 85 (1994) 419-428. [CrossRef] [MathSciNet]
  24. J.P. Mandallena, Contributions à une approche générale de la régularisation variationnelle de fonctionnelles intégrales, Thèse de Doctorat. Université de Montpellier II (1999).
  25. P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals. Manuscripta Math. 51 (1985) 1-28. [CrossRef] [MathSciNet]
  26. P. Marcellini and C. Sbordone, On the existence of minima of multiple integrals in the Calculus of Variations. J. Math. Pures Appl. 62 (1983) 1-9. [MathSciNet]
  27. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press, London (1995).
  28. C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer-Verlag, Berlin (1966).
  29. C. Olech, Weak lower semicontuity of integral functionals. J. Optim. Theory Appl. 19 (1976) 3-16. [CrossRef]
  30. T. O'Neil, A measure with a large set of tangent measures. Proc. Amer. Math. Soc. 123 (1995) 2217-2221. [MathSciNet]
  31. D. Preiss, Geometry of measures on Formula : Distribution, rectifiability and densities. Ann. Math. 125 (1987) 573-643.
  32. L. Simon, Lectures on Geometric Measure Theory. Australian Nat. Univ., Proc. Centre for Math. Anal. 3 (1983).
  33. M. Valadier, Multiapplications mesurables à valeurs convexes compactes. J. Math. Pures Appl. 50 (1971) 265-297. [MathSciNet]
  34. V.V. Zhikov, On an extension and an application of the two-scale convergence method. Mat. Sb. 191 (2000) 31-72.