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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 1, Pages 23–74 (Mi izv554)  

This article is cited in 25 scientific papers (total in 25 papers)

Homogenization of random singular structures and random measures

V. V. Zhikova, A. L. Piatnitskibc

a Vladimir State Pedagogical University
b P. N. Lebedev Physical Institute, Russian Academy of Sciences
c Narvik Institute of Technology

Abstract: The paper deals with the homogenization of random statistically homogeneous singular structures and variational problems involving integration with respect to ergodic stationary random measures.

DOI: https://doi.org/10.4213/im554

Full text: PDF file (788 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2006, 70:1, 19–67

Bibliographic databases:

UDC: 517.9
Received: 03.02.2005

Citation: V. V. Zhikov, A. L. Piatnitski, “Homogenization of random singular structures and random measures”, Izv. RAN. Ser. Mat., 70:1 (2006), 23–74; Izv. Math., 70:1 (2006), 19–67

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mathieu P., Piatnitski A., “Quenched invariance principles for random walks on percolation clusters”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463:2085 (2007), 2287–2307  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. 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
    3. Zhikov V.V., “Nash-Aronson Estimates for Solutions to Some Parabolic Equations: Application to Asymptotic Diffusion Problems”, Dokl. Math., 75:2 (2007), 247–251  crossref  mathscinet  zmath  isi  elib  scopus
    4. Faggionato A., “Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit”, Electron. J. Probab., 13 (2008), 2217–2247  crossref  mathscinet  zmath  isi  elib  scopus
    5. Amirat Y., Bodart O., Chechkin G.A., Piatnitski A.L., “Boundary homogenization in domains with randomly oscillating boundary”, Stochastic Process. Appl., 121:1 (2011), 1–23  crossref  mathscinet  zmath  isi  elib  scopus
    6. Sango M., Woukeng J.L., “Stochastic $\Sigma$-convergence and applications”, Dyn. Partial Differ. Equ., 8:4 (2011), 261–310  crossref  mathscinet  zmath  isi  elib  scopus
    7. Sango M., Woukeng J.L., “Stochastic two-scale convergence of an integral functional”, Asymptot. Anal., 73:1-2 (2011), 97–123  mathscinet  zmath  isi  elib
    8. Heida M., “An extension of the stochastic two-scale convergence method and application”, Asymptot. Anal., 72:1-2 (2011), 1–30  crossref  mathscinet  zmath  isi  elib  scopus
    9. V. V. Zhikov, “Estimates of the Nash–Aronson type for degenerating parabolic equations”, Journal of Mathematical Sciences, 190:1 (2013), 66–79  mathnet  crossref  mathscinet
    10. Fatima T., Muntean A., Ptashnyk M., “Unfolding-based corrector estimates for a reaction–diffusion system predicting concrete corrosion”, Applicable Analysis, 2012  crossref  mathscinet  zmath  isi  elib  scopus
    11. Alen Alexanderian, Muruhan Rathinam, Rouben Rostamian, “Homogenization, Symmetry, and Periodization in Diffusive Random Media”, Acta Mathematica Scientia, 32:1 (2012), 129  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Heida M., “Stochastic homogenization of heat transfer in polycrystals with nonlinear contact conductivities”, Applicable Analysis, 2012  crossref  mathscinet  isi  elib  scopus
    13. L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164  mathnet
    14. Moussa A.A., Zlaiji L., “Dimension Reduction and Homogenization of Random Degenerate Operators. Part I”, LMS J. Comput. Math., 15 (2012), 1–22  crossref  mathscinet  zmath  isi  elib  scopus
    15. Chechkin G.A., D'Apice C., De Maio U., Piatnitski A.L., “On the Rate of Convergence of Solutions in Domain with Random Multilevel Oscillating Boundary”, Asymptotic Anal., 87:1-2 (2014), 1–28  crossref  mathscinet  zmath  isi  scopus
    16. Bouchitte G., Bourel Ch., Manca L., “Resonant Effects in Random Dielectric Structures”, ESAIM-Control OPtim. Calc. Var., 21:1 (2015), 217–246  crossref  mathscinet  zmath  isi  scopus
    17. Ba M., Mathieu P., “a Sobolev Inequality and the Individual Invariance Principle For Diffusions in a Periodic Potential”, SIAM J. Math. Anal., 47:3 (2015), 2022–2043  crossref  mathscinet  zmath  isi  elib  scopus
    18. Piatnitski A., Zhikov V., “Homogenization of Random Navier–Stokes-Type System For Electrorheological Fluid”, J. Differ. Equ., 260:5 (2016), 4110–4129  crossref  mathscinet  zmath  isi  scopus
    19. Matzavinos A., Ptashnyk M., “Stochastic homogenization of the Keller–Segel chemotaxis system”, Nonlinear Anal.-Theory Methods Appl., 144 (2016), 58–76  crossref  mathscinet  zmath  isi  scopus
    20. Bukal M., Pawelczyk M., Velcic I., “Derivation of homogenized Euler–Lagrange equations for von Kármán rods”, J. Differ. Equ., 262:11 (2017), 5565–5605  crossref  mathscinet  zmath  isi  scopus
    21. Braides A., Cancedda A., Piat V.Ch., “Homogenization of Metrics in Oscillating Manifolds”, ESAIM-Control OPtim. Calc. Var., 23:3 (2017), 889–912  crossref  mathscinet  zmath  isi  scopus
    22. Heida M., “Stochastic Homogenization of Rate-Independent Systems and Applications”, Continuum Mech. Thermodyn., 29:3 (2017), 853–894  crossref  mathscinet  zmath  isi  scopus
    23. Heida M., Schweizer B., “Stochastic Homogenization of Plasticity Equations”, ESAIM-Control OPtim. Calc. Var., 24:1 (2018), 153–176  crossref  mathscinet  zmath  isi
    24. Neukamm S., Varga M., “Stochastic Unfolding and Homogenization of Spring Network Models”, Multiscale Model. Simul., 16:2 (2018), 857–899  crossref  mathscinet  zmath  isi  scopus
    25. A. M. Meirmanov, S. A. Gritsenko, “Homogenization of the equations of filtration of a viscous fluid in two porous media”, Siberian Math. J., 59:5 (2018), 909–921  mathnet  crossref  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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