Fibered microstructures for some nonlocal Dirichlet forms

 Access to full text

 Full (PDF)

1. [ 1 ] C. Amrouche - V. Girault, Decomposition of vector spaces and application to the stokes problem in arbitrary dimension, Czechoslovak Math. J.44 (1994), 109-140. Zbl0823.35140MR1257940
2. [2] H. Attouch, "Variational convergence for function and operators", Pitman, 1984. Zbl0561.49012MR773850
3. [3] M. Bellieud - G. Bouchitté, Homogenization of elliptic problems in a fiber reinforced structure. Nonlocal effects, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), 407-436. Zbl0919.35014MR1635769
4. [4] A. Beurling - J. Deny, Espaces de Dirichlet. I. Le cas élémentaire, Acta Math.99 (1958), 203-224. Zbl0089.08106MR98924
5. [5] A. Beurling - J. Deny, Dirichlet spaces, Proc. Nat. Acad. Sci. USA45 (1959), 208-215. Zbl0089.08201MR106365
6. [6] M E. BOGOVSKII, Solution of the first boundary value problem for an equation ofcontinuity of an incompressible medium, Dokl. Akad. Nauk SSSR248 (1979), 1037-1040. Zbl0499.35022MR553920
7. [7] G. Bouchitté - C. Picard, Singular perturbations and homogenization in stratified media, Appl. Anal.61 (1996), 307-341. Zbl0865.35013MR1618240
8. [8] D. Cioranescu - F. Murat, "Un terme étrange venu d' ailleurs", Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, 82. Zbl0496.35030
9. [9] G. Dal Maso - U. Mosco, Wiener's criterion and γ-convergence, Appl. Math. Optim.15 (1987), 15-63. Zbl0644.35033
10. [10] V.N. Fenchenko - E. Ya. Khruslov, The asymptotics of the solutions of differential equations with a strongly oscillating coefficient matrix not satisfying the condition of uniform limitation, Dokl. Akad. Nauk Ukrain. SSR Ser. A4 (1981), 23-27. Zbl0455.35010MR615994
11. [11] M. Fukushima, "Dirichlet forms and markov processes", North-Holland Math. Library23, North Holland, Amsterdam, 1980. Zbl0422.31007MR569058
12. [12] R. Gulliver - G. Dal Maso - U. Mosco, Asymptotic spectrum of manifolds of increasing topological type, to appear. 
13. [ 13] E. De Giorgi - T. Franzoni, Su un tipo di convergenza variazionale, part 1, Atti Accademia Nazionale dei Lincei, Rend. Cl. Sci. Mat. Fis. Natur., 1975. Zbl0339.49005
14. [14] E. De Giorgi - T. Franzoni, Su un tipo di convergenza variazionale, part 2, Rend. Sem. Mat. Brescia, 1979. MR458348
15. [15] E. Ya. Khruslov, Homogenized models of composite media, in Composite media and homogenization theory (Trieste, 1990), pages 159-182. BirkhäuserBoston, Boston, MA, 1991. Zbl0737.73009MR1145750
16. [16] Y. Lejan, Mesures associées a une forme de dirichlet. Applications, Bull. Soc. Math. France, 1978. Zbl0393.31008MR508949
17. [17] V.A. Marchenko - E. Ya. Khruslov, "Boundary value problems in domains with fine-grained boundaries", Naukova Dumka, Kiev, 1974. Zbl0289.35002
18. [18] G. Dal Maso, "An introduction to r-convergence", Birkhäuser Boston Inc., Boston, MA, 1993. Zbl0816.49001MR1201152
19. [19] G. Dal Maso - U. Mosco, Wiener criteria and energy decayfor relaxed dirichlet problems, Arch. Rat. Mech. Anal., 86. Zbl0634.35033
20. [20] U. Mosco, Some variational aspects of discontinuous media, Boll. Un. Mat. Ital.A (7), 7 (1993), 149-198. Zbl0802.35163MR1234068
21. [21] U. Mosco, Composite media and asymptotic Dirichlet forms, J. Funct. Anal., 123 (1994), 368-421. Zbl0808.46042MR1283033
22. [22] L. Tartar, Nonlocal effects induced by homogenization, in Partial differential equations and the calculus of variations, Vol. II, pages 925-938. BirkhäuserBoston, Boston, MA, 1989. Zbl0682.35028MR1034036

1. Marc Briane, Juan Casado-Díaz, Homogenization of systems with equi-integrable coefficients