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Averaging error for elliptic equations with “layered” random coefficients

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Literature Cited

  1. M. I. Friedlin, “The Dirichlet problem for the equations with periodic coefficients that depend on a small parameter,” Teor. Veroyatn. Primen.,9, No. 1, 133–139 (1964).

    Google Scholar 

  2. G. C. Papanicolaou and S. R. S. Varadhan, “Diffusions with random coefficients,” in: Statistics and Probability: Essays in Honor of C. R. Rao, North-Holland, Amsterdam (1982), pp. 547–552.

    Google Scholar 

  3. V. V. Yurinskii, “On the averaging of nondivergent equations of second order with random coefficients,” Sib. Mat. Zh.,23, No. 2, 176–188 (1982).

    Google Scholar 

  4. V. V. Zhikov and M. M. Sirazhudinov, “Averaging of nondivergent elliptic and parabolic operators of second order and stabilization of solutions of the Cauchy problem,” Mat. Sb.,116, No. 2, 166–186 (1981).

    Google Scholar 

  5. V. V. Yurinskii, “On the averaging of nondivergent random elliptic operators,” in: Limit Theorems of the Theory of Probability and Related Questions [in Russian], Trudy Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Vol. 1, Nauka, Novosibirsk (1982), pp. 126–138.

    Google Scholar 

  6. W. Feller, Introduction to Probability Theory and Its Application, Vol. II, Wiley, New York (1966).

    Google Scholar 

  7. M. V. Safonov, “The Harnack inequality for elliptic equations and the Hölder property of their solutions,” J. Sov. Math.,21, No. 5 (1983).

  8. M. Loeve, Probability Theory, Van Nostrand, Princeton (1955).

    Google Scholar 

  9. N. V. Krylov, Control Processes of Diffusion Type [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  10. S. A. Utev, “Probability inequalities for sums of weakly dependent random variables (abstract of a report),” Teor. Veroyatn. Primen.,27, No. 1, 201 (1982).

    Google Scholar 

  11. N. S. Bakhvalov, “Averaging of partial differential equations with fast-oscillating coefficients,” Dokl. Akad. Nauk SSSR,221, No. 3, 516–519 (1975).

    Google Scholar 

  12. D. G. Aronson and J. Serrin, “Local behavior of solutions of quasilinear parabolic equations,” Arch. Ration. Mech. Anal.,25, No. 2, 81–122 (1967).

    Google Scholar 

  13. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).

  14. A. D. Aleksandrov, “Majorization of solutions of second-order linear equations,” Vestn. Leningr. Univ., Ser. Mat., Mekh., Astron., No. 1, 5–25 (1966).

    Google Scholar 

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Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 2, pp. 176–186, March–April, 1985.

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Yurinskii, V.V. Averaging error for elliptic equations with “layered” random coefficients. Sib Math J 26, 300–309 (1985). https://doi.org/10.1007/BF00968777

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