Literature Cited
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).
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.
V. V. Yurinskii, “On the averaging of nondivergent equations of second order with random coefficients,” Sib. Mat. Zh.,23, No. 2, 176–188 (1982).
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).
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.
W. Feller, Introduction to Probability Theory and Its Application, Vol. II, Wiley, New York (1966).
M. V. Safonov, “The Harnack inequality for elliptic equations and the Hölder property of their solutions,” J. Sov. Math.,21, No. 5 (1983).
M. Loeve, Probability Theory, Van Nostrand, Princeton (1955).
N. V. Krylov, Control Processes of Diffusion Type [in Russian], Nauka, Moscow (1977).
S. A. Utev, “Probability inequalities for sums of weakly dependent random variables (abstract of a report),” Teor. Veroyatn. Primen.,27, No. 1, 201 (1982).
N. S. Bakhvalov, “Averaging of partial differential equations with fast-oscillating coefficients,” Dokl. Akad. Nauk SSSR,221, No. 3, 516–519 (1975).
D. G. Aronson and J. Serrin, “Local behavior of solutions of quasilinear parabolic equations,” Arch. Ration. Mech. Anal.,25, No. 2, 81–122 (1967).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).
A. D. Aleksandrov, “Majorization of solutions of second-order linear equations,” Vestn. Leningr. Univ., Ser. Mat., Mekh., Astron., No. 1, 5–25 (1966).
Additional information
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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DOI: https://doi.org/10.1007/BF00968777