Two-scale convergence and homogenization on BV(Ω)

Asymptotic Analysis

Volumn 16, Issue 1, 1998, Pages 65-84

  Amar, M ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

2 Scale convergence; BV functions; Homogenization; Measures

Indexed keywords

EID: 0005753673     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. G. Allaire, Homogénéisation et convergence à deux échelles, application à un problème de convection diffusion, C. R. Acad. Sci. Paris 312 (1991), 581-586.
2. G. Allaire, Homogenization of the unsteady Stokes equations in porous media, in: Progress in Partial Differential Equations: Calculus of Variations, Applications, C. Bandle et al., eds, Pitman Res. Notes in Math., Series 2671, Longman Higher Education, New York, 1992, pp. 109-123.
3. G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal. 23(6) (1992), 1482-1518.
4. M. Amar and E. Vitali, Homogenization of periodic Riemannian metrics, Preprint IAN, 1995 (to appear in J. Convex Anal.).
5. A. Bensoussan, J.L. Lions and G. Papanicolau, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
6. G. Bouchitté, Convergence et relaxation de fonctionelles du calcul des variations à croissance linéaire. Application à l'homogénéisation en plasticité, Annales Fac. des Sciences de Toulouse VII (1986), 7-36.
7. G. Bouchitté and P. Suquet, Charges limites, plasticité et homogénéisation: le cas d' un bord charge, C. R. Acad. Sci. Paris (I) 305 (1987), 441-444.
8. A. Braides, Homogenization of some almost periodic functional, Rend. Accad. Naz. Sci. XL (IX) 103 (1985), 313-322.
9. A. Braides, A homogenization theorem for weakly almost periodic functionals, Rend. Accad. Naz. Sci. XL (X) 104 (1986), 261-281.
10. A. Braides and V. Chiadò Piat, A derivation formula for convex integral functionals defined on BV(Q), J. Conv. Anal. 2 (1995), 69-85.
11. H. Brezis, Analyse Fonctionelle. Théorie et Applications, Masson, Paris, 1983.
12. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation Problems in the Calculus of Variations, Pitman Res. Notes in Math., Longman, Harlow, 1989.
13. G.Dal Maso, An Introduction to Γ-convergence, Birkhäuser, Boston, 1993.
14. R. De Arcangelis and G. Gargiulo, Homogenization of integral functionals with linear growth defined on vector-valued functions, Nonlinear Diff. Eq. Appl. 2 (1995), 371-416.
15. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58(8) (1975), 842-850.
16. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale, Rend. Sem. Mat. Brescia 3 (1979), 63-101.
17. N. Dunford and J. T. Schwartz, Linear Operators, Interscience, New York, 1957.
18. W. E, Homogenization of linear and nonlinear transport equations, Comm. Pure Appl. Math. 45 (1992), 301-326.
19. L.C. Evans and R.F. Gariepy, Lecture Notes on Measure. Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992.
20. W. Feller, An Introduction to Probability Theory and Its Applications, Vols I, II, Wiley New York 1960.
21. M. Giaquinta, G. Modica and J. Soucek, Functionals with linear growth in the calculus of variations. I, Comment. Math. Univ. Carolin. 20 (1979), 143-156.
22. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkäuser, Boston 1984.
23. C. Goffman and J. Serrin, Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964), 159-178.
24. J.L. Lions, Some Methods in the Mathematical Analysis of Systems and Their Controls, Science Press, Beijing, Gordon and Breach, New York, 1981.
25. S. Luckhaus and L. Modica, The Gibbs-Thomson relation within the gradient theory of phase transitions, Arch. Rat Mech. An. 1 (1989), 71-83.
26. V.G. Maz'ya, Sobolev Spaces, Springer, Berlin, 1985.
27. S. Müller, Homogenization of nonconvex integral functionals and cellular elastic materials Arch Rat Mech An 99 (1987). 189-212.
28. J. Neveu, Bases Mathématiques du Calcul des Probabilités, Masson, Paris, 1980.
29. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989), 608-623.
30. G. Nguetseng, Asymptotic analysis for a stiff variational problem arising in mechanics. SIAM J. Math. Anal. 21 (1990), 1394-1414.
31. M.M. Rao, Conditional Measures and Applications, Dekker, New York, 1993.
32. Yu.G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math. J. 9 (1968), 1039-1045.
33. R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1972.
34. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
35. L. Schwartz, Théorie des Distributions, Hermann, Paris, 1966.
36. L. Schwartz, Lectures on Disintegration of Measures, Notes of S. Ramaswamy, Tata Institute of Fundamental Research, Bombay, 1975.
37. M. Valadier, Two-scale convergence and Young measures, Prèpublication no. 02, Départ. de Math., Université de Montpellier, France, 1995.
38. M. Valadier, Admissible functions and two-scale convergence, Prèpublication, Départ, de Math., Université de Montpellier, France, 1995.
39. A.I. Vol'pert and S.I. Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Martinus Nijhoff Publishers, Dordrecht, 1985.