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Mat. Sb., 1996, Volume 187, Number 8, Pages 3–40 (Mi msb150)  

This article is cited in 55 scientific papers (total in 55 papers)

Connectedness and homogenization. Examples of fractal conductivity

V. V. Zhikov

Vladimir State Pedagogical University

Abstract: 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.

DOI: https://doi.org/10.4213/sm150

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English version:
Sbornik: Mathematics, 1996, 187:8, 1109–1147

Bibliographic databases:

UDC: 517.9
MSC: Primary 35B27, 28A75; Secondary 28A80
Received: 27.09.1995

Citation: V. V. Zhikov, “Connectedness and homogenization. Examples of fractal conductivity”, Mat. Sb., 187:8 (1996), 3–40; Sb. Math., 187:8 (1996), 1109–1147

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. V. V. Zhikov, “Weighted Sobolev spaces”, Sb. Math., 189:8 (1998), 1139–1170  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. V. Zhikov, “On the Homogenization Technique for Variational Problems”, Funct. Anal. Appl., 33:1 (1999), 11–24  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. V. Sandrakov, “Homogenization of elasticity equations with contrasting coefficients”, Sb. Math., 190:12 (1999), 1749–1806  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Beliaev, A, “The homogenization of Stokes flows in random porous domains of general type”, Asymptotic Analysis, 19:2 (1999), 81  mathscinet  zmath  isi  elib
    5. V. V. Zhikov, “On an extension of the method of two-scale convergence and its applications”, Sb. Math., 191:7 (2000), 973–1014  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. O. M. Penkin, E. M. Bogatov, “Weak Solvability of the Dirichlet Problem on Stratified Sets”, Math. Notes, 68:6 (2000), 740–750  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Guy Bouchitté, Ilaria Fragalà, “Homogenization of Thin Structures by Two-Scale Method with Respect to Measures”, SIAM J Math Anal, 32:6 (2001), 1198  crossref  mathscinet  zmath  isi  scopus  scopus
    8. S. E. Pastukhova, “Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain”, Sb. Math., 192:2 (2001), 245–260  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Jikov, VV, “On two types of effective conductivities”, Journal of Mathematical Analysis and Applications, 256:1 (2001), 339  crossref  mathscinet  zmath  isi
    10. S. B. Shulga, “Homogenization of Nonlinear Variational Problems by Means of Two-Scale Convergence”, Proc. Steklov Inst. Math., 236 (2002), 357–364  mathnet  mathscinet  zmath
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    12. Kulyaba, VV, “Poincaré's inequality on stratified sets”, Doklady Mathematics, 66:2 (2002), 220  zmath  isi  elib
    13. Briane, M, “Homogenization in general periodically perforated domains by a spectral approach”, Calculus of Variations and Partial Differential Equations, 15:1 (2002), 1  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    14. Franchi, B, “Two-scale homogenization in the Heisenberg group”, Journal de Mathematiques Pures et Appliquees, 81:6 (2002), 495  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. Damlamian, A, “Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?”, ESAIM-Control Optimisation and Calculus of Variations, 8 (2002), 555  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    16. Briane, M, “Homogenization of a class of non-uniformly elliptic monotonic operators”, Nonlinear Analysis-Theory Methods & Applications, 48:1 (2002), 137  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    17. V. V. Kulyaba, O. M. Penkin, “The Maximum Principle for Parabolic Inequalities on Stratified Sets”, Math. Notes, 73:2 (2003), 228–239  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. V. V. Shumilova, “On the Homogenization of a Problem with Two Small Parameters in Double-Porosity Media”, Math. Notes, 74:5 (2003), 753–756  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    22. Casado-Diaz, J, “Homogenization of the anisotropic heterogeneous linearized elasticity system in thin reticulated structures”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 134 (2004), 1041  crossref  mathscinet  zmath  isi  elib
    23. Braides, A, “A variational approach to double-porosity problems”, Asymptotic Analysis, 39:3–4 (2004), 281  mathscinet  zmath  isi  elib
    24. Nazarov, SA, “Branching periodicity: Homogenization of the Dirichlet problem for an elliptic system”, Doklady Mathematics, 70:1 (2004), 628  mathscinet  zmath  isi  elib
    25. Nicaise, S, “Poincaré-Perron's method for the Dirichlet problem on stratified sets”, Journal of Mathematical Analysis and Applications, 296:2 (2004), 504  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    26. Kulyaba, VV, “Strong stratified sets and the Friedrichs inequality”, Differential Equations, 40:1 (2004), 75  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    27. V. V. Zhikov, “Spectral Method in Homogenization Theory”, Proc. Steklov Inst. Math., 250 (2005), 85–94  mathnet  mathscinet  zmath
    28. Proc. Steklov Inst. Math., 250 (2005), 245–253  mathnet  mathscinet  zmath
    29. S. A. Nazarov, A. S. Slutskij, “Averaging of an elliptic system under condensing perforation of a domain”, St. Petersburg Math. J., 17:6 (2006), 989–1014  mathnet  crossref  mathscinet  zmath  elib
    30. A. V. Komarov, O. M. Penkin, “On Spectra of a Nonperiodic Woven Membrane”, Journal of Mathematical Sciences (New York), 133:1 (2006), 883  crossref  mathscinet  zmath  elib  scopus  scopus
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    33. Shumilova, VV, “On one property of two-scale convergence”, Differential Equations, 42:1 (2006), 155  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    34. S. E. Pastukhova, “Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems”, Sb. Math., 198:10 (2007), 1465–1494  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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    37. A. M. Meirmanov, “Acoustic and filtration properties of a thermoelastic porous medium: Biot's equations of thermo-poroelasticity”, Sb. Math., 199:3 (2008), 361–384  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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