no. 4
A homogenization result for planar, polygonal networks
ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 4, pp. 483-514. 
@article{M2AN_1991__25_4_483_0,
     author = {Vogelius, Michael},
     title = {A homogenization result for planar, polygonal networks},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {483--514},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {25},
     number = {4},
     year = {1991},
     mrnumber = {1108587},
     zbl = {0737.35126},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1991__25_4_483_0/}
}
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Vogelius, Michael. A homogenization result for planar, polygonal networks. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 4, pp. 483-514. http://archive.numdam.org/item/M2AN_1991__25_4_483_0/

[1] D. N. Arnold, L. Ridgway Scott and M. Vogelius, Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon, Ann. Scuola Norm. Sup. Pisa, 15 (1988), pp. 169-192. | Numdam | MR | Zbl

[2] H. Attouch and G. Buttazzo, Homogenization of reinforced periodic one-codimensional structures, Ann. Scuola Norm. Sup. Pisa, 14(1987), pp. 465-484. | Numdam | MR | Zbl

[3] D. Aze and G. Buttazzo, Some remarks on the optimal design of periodically reinforced structures, RAIRO Model. Math. Anal. Numer., 23 (1989), pp. 53-61. | Numdam | MR | Zbl

[4] J. Bramble and M. Zlamal, Triangular elements in the finite element method, Math. Comp., 24 (1970), pp. 809-820. | MR | Zbl

[5] G. Buttazzo and G. Dal Maso, Γ-limits of integral functionals, J. Analyse Math., 37 (1980), pp. 145-185. | MR | Zbl

[6] E. Degiorgi and S. Spagnolo, Sulla convergenza degli integrali dell'energia per operatori ellitici del secundo ordine, Boll. U.M.I., 8 (1973), pp. 391-411. | MR | Zbl

[7] R. J. Duffin, Distributed and lumped networks, J. Math. Mech., 8 (1959), pp. 793-825. | MR | Zbl

[8] R. J. Duffin, Extremal length of a network, J. Math. Anal. Appl., 5 (1962), pp. 200-215. | MR | Zbl

[9] R. J. Duffin, Topology of series-parallel networks, J. Math. Anal. Appl., 10 (1965), pp. 303-318. | MR | Zbl

[10] R. J. Duffin, Estimating Dirichlet's integral and electrical conductance for systems which are not self-adjoint. Arch. Rat. Mech. Anal., 30 (1968), pp. 90-101. | MR | Zbl

[11] P. Grisvard, Elliptic problems in Nonsmooth Domains, Pitman, Marshfield, MA, 1985. | MR | Zbl

[12] P.-O. Jansson and G. Grimwall, Joule heat distribution in disordered resistor networks, J. Phys. D: Appl. Phys., 18 (1985), pp. 893-900.

[13] R. Künnemann, The diffusion limit for reversible jump processes on Zd with ergodic random bond conductivities. Comm. Math. Phys., 90 (1983), pp. 27-68. | MR | Zbl

[14] K. A. Lurie and A. V. Cherkaev, G-closure of a set of anisotropically conducting media in the two dimensional case. J. Opt. Th. Appl., 42 (1984), pp. 283-304. | MR | Zbl

[15] K. A. Lurie and A. V. Cherkaev, Exact estimates of the conductivity of composites formed by two materials taken in prescribed proportion. Proc. Roy. Soc. Edinburgh, 99 A (1984), pp. 71-87. | MR | Zbl

[16] F. Murat, H-convergence, Mimeographed notes, Université d'Alger, 1978.

[17] F. Murat and L. Tartar, Calcul des variations et homogeneisation, In Les Méthodes de l'Homogénéization : Théorie et Applicationsen Physique ; proc. of summer school on homogenization, Breau-sans-Nappe, July 1983 ; Eyrolles, Paris, 1985, pp. 319-369. | MR

[18] J. A. Nitsche and A. H. Schatz, Interior estimates for Ritz-Galerkun methods. Math. Comp., 28 (1974), pp. 937-958. | MR | Zbl

[19] G. Papanicolaou and S. R. S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Coll. Math. Societatis János Bólyai, #27, Esztergom, Hungary, pp. 835-873, North-Holland, Amsterdam, 1982. | MR | Zbl

[20] M. Soderberg, P.-O. Jansson and G. Grimwall, Effective medium theory for resistor networks in checkerboard geometres. J. Phys. A. Math. Gen., 18 (1985), pp. L633-L636.

[21] L. Tartar, Estimations fines des coefficients homogénéisés, In Ennio De-Giorgi's Colloquium, P. Krée, ed., Pitman Press, London, 1985. | MR | Zbl