Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.N.Bogolyubov, On some statistical methods in mathematical physics. Acad. Nauk Ukrain. SSR, L'vov, 1945, MR 8-37.
S.Poisson, Seconde memoire sur la theorie du magnetisme, Mèm. De l'Acad. de France 1882, 5.
J.C. Maxwell, Electricity and Magnetism, vol.1, Clarendon Press, Oxford, 1892.
W.R.Rayleigh, On the influence of obstacles arranged in rectangular order upon the properties of a medium. Phys.Mag.34 (1892), 241, 481.
A.Bensoussan, J.L.Lions, G.Papanicolaou, Asymptotic analysis for periodic structures North Holland, Amsterdam, 1978.
J.L.Lions, Some methods in the mathematical analysis of systems and their control, Science Press, Beijing, China, Gordon and Breach Inc. New York, 1981.
E.Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Physics, 127, Springer Verlag, 1980.
S.M. Kozlov, O.A. Oleinik, V.V. Zhikov, Kha T'en Ngoan, Averaging and G-convergence of differential operators, Russian Math. Surveys, 34:5 (1979), 69–147.
S.M. Kozlov, O.A. Oleinik, V.V. Zhikov, On G-convergence of parabolic operators, Russian Math. Surveys, 36:1 (1981).
E. De Giorgi, S. Spagnolo, Sulla convergenca degli integrali dell' energia per operatori ellittici del 2 ordine, Boll. Un. Mat. Ital. (4), 8 (1973) 391–411, MR 50 880.
S.Spagnolo, Convergence in energy for elliptic operators, Proc. third Sympos. Numer. Solut. Partial differential equations, College Park, Md., (1976), 469–498.
P. Marcellini, Convergence of second order linear elliptic operators, Boll. Un. Mat. Ital., B(5) 15 (1979).
S.M.Kozlov, Asymptotics at the infinity for fundamental solutions of equations with almost periodic coefficients, Vestnik Mosc. Univ. ser. 1, Mat., Mech. no 4, 1980, 11–16.
S.M. Kozlov, Asymptotics of fundamental solutions of divergent second order equations, Matem. Sbornik, 113:2, (1982), 302–323.
O.A.Oleinik, V.V.Zhikov, On the homogenization of elliptic operators with almost periodic coefficients In “Proceedings of the International meeting dedicated to Prof. Amerio”, Milano, 1983.
S.M. Kozlov, O.A. Oleinik, V.V. Zhikov, Homogenization of parabolic operators. Trudi Mosc. Mat. Ob. v.45, 182–236, (1982).
S.M. Kozlov, O.A. Oleinik, V.V. Zhikov, Theorems on the homogenization of parabolic operators, Dokl. Akad. Nauk SSSR, 260:3, (1981).
S.M.Kozlov O.A.Oleinik, V.V.Zhikov, Sur l'homogeneisation d'operateurs differentiels paraboliques a coefficients presque-periodiques, C.R.Acad Sc. Paris t.293, ser.1 (1981) 245–248.
S.M. Kozlov, O.A. Oleinik, V.V. Zhikov, Homogenization of parabolic operators with almost periodic coefficients. Mat. Sbornik, 117:1 (1982), 69–85.
O.A.Oleinik, Homogenization of differential operators. In “Proceedings of the Conference held in Bratislava, 1981, Teubner-Texte zur Mathematik Band 47, Leipzig, 1982, 284–287.
O.A.Oleinik, V.V.Zhikov, On homogenization of the elasticity system with almost periodic coefficients, Vestn. Mosc. Univ., ser.1, Mat., Mech.,, 1982, no 6, 62–70.
O.A. Oleinik, G.P. Panasenko, G.A. Yosifian, Homogenization and asymptotic expansions for solutions of the elasticity system with rapidly oscillating periodic coefficients, Applicable Analysis, (1983), v.15, no 1-4, 15–32.
O.A. Oleinik, G.P. Panasenko, G.A. Yosifian, Asymptotic expansion of a solution of the elasticity system with periodic rapidly oscillating coefficients, Dokl. AN SSSR, (1982), v.266, no 1, 18–22
O.A. Oleinik, G.P. Panasenko, G.A. Yosifian, Asymptotic expansion for solutions of the elasticity system in perforated domains, Matem. Sbornik, (1983), v.120, no 1. 22–41.
O.A. Oleinik, G.A. Yosifian, An estimate for the deviation of the solution of the system of elasticity in a perforated domain from that of the averaged system, Russian Mathem Surveys, v.37, no 5, (1982), 188–189.
O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Homogenization of eigenvalues of a boundary value problem of the theory of elasticity with rapidly oscillating coefficients, Sibirsk. Matem. Journ., (1983) v.24, no 5, 50–58.
O.A.Oleinik, A.S.Shamaev, G.A.Yosifian, Homogenization of eigenvalues and eigenfunctions of the boundary value problem of elasticity in a perforated domain. Vestnik Mosc. Univ., ser.1, Mat., Mech.,, 1983, no 4, 53–63.
O.A.Oleinik, A.S.Shamaev, G.A.Yosifian. On the convergence of the energy, stress tensors and eigenvalues in homogenization problems of elasticity. Zeitschrift für Angew. Math. Mech., (1984)
O.A.Oleinik, A.S.Shamaev, G.A.Yosifian, On the convergence of the energy, stress tensors and eigenvalues in homogenization problems arising in elasticity, Dokl. AN SSSR, 1984
O.A. Oleinik, G.A. Yosifian, On the asymptotic behaviour at infinity of solutions in linear elasticity, Archive Rat. Mech. and Analysis, 1982, v.78, 29–53.
L.Tartar, Homogenization, Cours Peccot au College de France. Paris, 1977.
J.L. Lions, Asymptotic expansions in perforated media with a periodic structure, The Rocky Mountain Journ. of Math., 1980, v.10, no 1, 125–140.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Oleinik, O.A. (1984). On homogenization problems. In: Ciarlet, P.G., Roseau, M. (eds) Trends and Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12916-2_61
Download citation
DOI: https://doi.org/10.1007/3-540-12916-2_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12916-5
Online ISBN: 978-3-540-38800-5
eBook Packages: Springer Book Archive