Geodesic
Connectedness and homogenization. Examples of fractal conductivity
Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1109-1147 Cet article a éte moissonné depuis la source Math-Net.Ru

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A detailed study of the concept of $p$-connectedness is carried out; in particular, a criterion for the $p$-connectedness of two disjoint domains with Lipschitz boundaries and with fractal contact is formulated. New examples of open periodic sets with positive effective conductivity are constructed on the basis of this analysis. A new class of objects, elliptic operators in a Euclidean space with measure, is introduced; the corresponding concept of $p$-connectedness is introduced and a generalized theory of homogenization is developed. 
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     author = {V. V. Zhikov},
     title = {Connectedness and homogenization. {Examples} of fractal conductivity},
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     year = {1996},
     volume = {187},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_8_a0/}
}
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V. V. Zhikov. Connectedness and homogenization. Examples of fractal conductivity. Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1109-1147. http://geodesic.mathdoc.fr/item/SM_1996_187_8_a0/

[1] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Nauka, M., 1993 | MR | Zbl

[2] Oleinik O. A., Iosifyan G. A., Shamaev A. S., Matematicheskie zadachi teorii silno neodnorodnykh sred, MGU, M., 1990

[3] Zhikov V. V., “Ob usrednenii v perforirovannykh sluchainykh oblastyakh obschego vida”, Matem. zametki, 53:1 (1993), 41–58 | MR | Zbl

[4] Zhikov V. V., “On the Homogenization of Nonlinear Variational Problems in perforated Domains”, Russian J. Math. Phys., 2:3 (1994), 393–408 | MR | Zbl

[5] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR | Zbl

[6] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[7] Mazya V. G., Poborchii S. V., “Prodolzhenie iz klassov S. L. Soboleva vo vneshnosti oblasti s vershinoi pika na granitse, I”, Czechoslovak Math. J., 36 (111) (1986), 634–661 | MR | Zbl

[8] Evans L. C., Gariepy R. F., Measure theory and fine properties of functions, CRC PRESS, London, 1992 | MR | Zbl

[9] Barlow M. T., Bass R. F., “On the resistans of the Sierpinski carpet”, Proc. Roy. Soc. London Ser. A, 431:1882 (1990), 345–360 | DOI | MR | Zbl

[10] Kozlov S. M., “Harmonization and homogenization on Fractals”, Commun. Math. Phys., 153 (1993), 339–357 | DOI | MR | Zbl

[11] Gelbaum B., Olmsted Dzh., Kontrprimery v analize, Mir, M., 1967 | Zbl