@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://www.numdam.org/item/M2AN_1991__25_4_483_0/} }
TY - JOUR AU - Vogelius, Michael TI - A homogenization result for planar, polygonal networks JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1991 SP - 483 EP - 514 VL - 25 IS - 4 PB - AFCET - Gauthier-Villars PP - Paris UR - http://www.numdam.org/item/M2AN_1991__25_4_483_0/ LA - en ID - M2AN_1991__25_4_483_0 ER -
%0 Journal Article %A Vogelius, Michael %T A homogenization result for planar, polygonal networks %J ESAIM: Modélisation mathématique et analyse numérique %D 1991 %P 483-514 %V 25 %N 4 %I AFCET - Gauthier-Villars %C Paris %U http://www.numdam.org/item/M2AN_1991__25_4_483_0/ %G en %F M2AN_1991__25_4_483_0
Vogelius, Michael. A homogenization result for planar, polygonal networks. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 4, pp. 483-514. http://www.numdam.org/item/M2AN_1991__25_4_483_0/
[1] 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
, and ,[2] Homogenization of reinforced periodic one-codimensional structures, Ann. Scuola Norm. Sup. Pisa, 14(1987), pp. 465-484. | Numdam | MR | Zbl
and ,[3] Some remarks on the optimal design of periodically reinforced structures, RAIRO Model. Math. Anal. Numer., 23 (1989), pp. 53-61. | Numdam | MR | Zbl
and ,[4] Triangular elements in the finite element method, Math. Comp., 24 (1970), pp. 809-820. | MR | Zbl
and ,[5] Γ-limits of integral functionals, J. Analyse Math., 37 (1980), pp. 145-185. | MR | Zbl
and ,[6] Sulla convergenza degli integrali dell'energia per operatori ellitici del secundo ordine, Boll. U.M.I., 8 (1973), pp. 391-411. | MR | Zbl
and ,[7] Distributed and lumped networks, J. Math. Mech., 8 (1959), pp. 793-825. | MR | Zbl
,[8] Extremal length of a network, J. Math. Anal. Appl., 5 (1962), pp. 200-215. | MR | Zbl
,[9] Topology of series-parallel networks, J. Math. Anal. Appl., 10 (1965), pp. 303-318. | MR | Zbl
,[10] 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] Elliptic problems in Nonsmooth Domains, Pitman, Marshfield, MA, 1985. | MR | Zbl
,[12] Joule heat distribution in disordered resistor networks, J. Phys. D: Appl. Phys., 18 (1985), pp. 893-900.
and ,[13] 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] 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
and ,[15] 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
and ,[16] H-convergence, Mimeographed notes, Université d'Alger, 1978.
,[17] 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
and ,[18] Interior estimates for Ritz-Galerkun methods. Math. Comp., 28 (1974), pp. 937-958. | MR | Zbl
and ,[19] 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
and ,[20] Effective medium theory for resistor networks in checkerboard geometres. J. Phys. A. Math. Gen., 18 (1985), pp. L633-L636.
, and ,[21] Estimations fines des coefficients homogénéisés, In Ennio De-Giorgi's Colloquium, P. Krée, ed., Pitman Press, London, 1985. | MR | Zbl
,