Multi-scale young measures

Transactions of the American Mathematical Society

Volumn 358, Issue 2, 2006, Pages 591-602

  Pedregal, Pablo ^a  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Multi scale convergence; Slicing measures; Young measures

Indexed keywords

EID: 33644519064     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03669-X     Document Type: Article

References (20)

1. G. Alberti, and S. Müller, A new approach to variational problems with multiple scales, Comm. Pure Appl. Math., 54 (2001), 761-825. MR2002f:49016
2. G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518. MR93k:35022
3. G. Allaire, and M. Briane, Multiscale convergence and reiterated homogenization, Proc. Roy. Soc. Edinburgh, 126A (1996), 297-342. MR97d:35014
4. L. Ambrosio, N. Fusco, and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, Oxford Universit Press, 2000. MR2003a:49002
5. E. J. Balder, Lectures on Young Measures, Cahiers de Mathématiques de la Décision No. 9517, CEREMADE, Université Paris IX, 1995.
6. E. J. Balder, On compactness results for multi-scale convergence, Proc. Royal Soc. Edinb., 129A (1999), 467-476. MR2001c:35026
7. J. M. Ball, 1989 A version of the fundamental theorem for Young measures, PDE's and continuum models of phase transitions, Lecture Notes in Physics, 344 (1989), (M. Rascle, D. Serre, and M. Slemrod, eds.) Springer-Verlag, pp. 207-215. MR91c;49021
8. A. Braides, and A. Defranceschi, 1998 Homogenization of multiple integrals, Oxford Lectures Series in Mathematics and its Applications, 12, Oxford University Press, 1998. MR2000g:49014
9. J. Casado Diaz, and I. Gayte, A general compactness result and its application to the two-scale convergence of almost periodic functions, C. R. Acad. Sci. Paris, 323 (1996), I, 329-334. MR97d:46095
10. D. Cioranescu, A. Damlamian, and G. Griso, Periodic unfolding and homogenization, C. R. Math. Acad. Sc.i Paris, 335 (2002), no 1, 99-104. MR2003g:35009
11. B. Dacorogna, Direct methods in the Calculus of Variations, Springer-Verlag, New York, 1989. MR90e:49001
12. W. E, Homogenization of linear and non-linear transport equations, Comm. Pure Appl. Math., 45 (1992), 301-326. MR92k:35026
13. L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS 74, American Mathematical Society, 1990. MR91a:35009
14. M. L. Mascarenhas, A. M. Toader, Scale convergence in homogenization, Numer. Funct. Anal. Opt., 22 (2001), 127-158. MR2003c:49023
15. S. Müller, Variational models for microstructure and phase transitions, Springer Lecture Notes in Math., 1713 (1999), pp. 85-210. MR2001b:49019
16. P. Pedregal, 1997 Parametrized Measures and Variational Principles, Birkhauser, Basel, 1997. MR98e:49001
17. P. Pedregal, P. Relaxation in magnetostriction, Calc. Var, 10 (2000), 1-19. MR2002d:49016
18. L. Tartar, Beyond Young measures, Meccanica, 30 (1995), 505-526. MR97c:49045
19. A. M. Toader, Links between Young measures associated with constrained sequences, ESAIM Cont. Opt. Calc. Var., 5 (2000), 579-590. MR2001m:28005
20. M. Valadier 1990 Young measures, Methods of Nonconvex Analysis, Lect. Notes in Math., 1446 (1990), Springer-Verlag, pp. 152-188 MR91j:28006