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Averaging of nondivergent second-order equations with random coefficients

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Literature Cited

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

    Google Scholar 

  2. S. M. Kozlov, “Averaging of differential operators with almost periodic fast oscillating coefficients,” Mat. Sb.,107, No. 2, 199–217 (1978).

    Google Scholar 

  3. A. Bensoussan, J. L. Lions, and G. Papanicolaou, “Homogeneization and ergodic theory,” Probability Theory, Banach Center Publications,5, 15–25, PWN, Warsaw (1979).

    Google Scholar 

  4. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, and Ha Tien Ngoan, “Averaging and G-convergence of differential operators,” Usp. Mat. Nauk,34, No. 6, 65–133 (1979).

    Google Scholar 

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

    Google Scholar 

  6. A. Bensoussan, J. L. Lions, and G. Papanicolaou, “Sur quelques phénomènes asymptotiques s stationnaires,” C. R. Acad. Sci. Paris,281, Nos. 2-3, A89-A94 (1975).

    Google Scholar 

  7. A. A. Tempel'man, “Ergodic theorems for general dynamic systems,” Tr. Mosk. Mat. Obsh.,26, 95–132 (1972).

    Google Scholar 

  8. R. Z. Khas'minskii, “Ergodic properties of reversible diffusion processes and stabilization of Cauchy's problem for parabolic equations,” Teor. Veroyatn. Ee Primen.,5, No. 2, 196–214 (1960).

    Google Scholar 

  9. 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 

  10. N. V. Krylov, “Some bounds for the distribution density of a stochastic integral,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 1, 228–248 (1974).

    Google Scholar 

  11. N. V. Krylov, Controlled Diffusion Processes [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  12. A. D. Aleksandrov, “Uniqueness conditions and bounds for the solution of Dirichlet's problem,” Vestn. Leningr. Univ., Ser. Mat., Mekh., Astron.,13, No. 3, 5–29 (1963).

    Google Scholar 

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

  14. A. I. Koshelev, “On the boundedness in Lp of the derivatives of the solutions of elliptic differential equations,” Mat. Sb.,38, No. 3, 278–312 (1956).

    Google Scholar 

  15. D. Greco, “New integral bounds for the solutions of a linear elliptic equation and applications to potential theory,” Ricerche Mat.,5, No. 1, 126–149 (1956).

    Google Scholar 

  16. N. V. Krylov, “Sequences of convex functions and bounds for the maximum of the solution of a parabolic equation,” Sib. Mat. Zh.,17, No. 2, 290–303 (1976).

    Google Scholar 

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Authors
  1. V. V. Yurinskii
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Additional information

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 23, No. 2, pp.176–188, March–April, 1982.

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Yurinskii, V.V. Averaging of nondivergent second-order equations with random coefficients. Sib Math J 23, 276–287 (1982). https://doi.org/10.1007/BF00971701

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