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$$G$$-closure of a set of anisotropically conducting media in the two-dimensional case. (English) Zbl 0504.73060
This paper deals with the problem of the invariant description of a set of conducting materials which may be obtained from some given initial compounds by the process of mixing. Complete solution to this problem is provided for a two-dimensional case.

##### MSC:
 74P99 Optimization problems in solid mechanics 74E30 Composite and mixture properties 74E10 Anisotropy in solid mechanics
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##### References:
 [1] Bensoussan, A., Lions, J. L., andPapanicolaou, G.,Asymptotic Analysis for Periodic Structures, North-Holland Publishing Company, Amsterdam, Holland, 1978. · Zbl 0404.35001 [2] Lurie, K. A., Cherkaev, A. V., andFedorov, A. V.,Regularization of Optimal Design Problems for Bar and Plates, Part 1, Journal of Optimization Theory and Applications, Vol. 37, No. 4, 1982. · Zbl 0464.73109 [3] Lurie, K. A., Cherkaev, A. V., andFedorov, A. V.,Regularization of Optimal Design Problems for Bar and Plates, Part 2, Journal of Optimization Theory and Applications, Vol. 37, No. 4, 1982. · Zbl 0464.73109 [4] Zhikov, V. V., Kozlov, S. M., Oleinik, O. A., andNgoan, K. T.,Homogenization and G-Convergence of Differential Operators (in Russian), Uspekhi Matematicheskikh Nauk, Vol. 34, No. 5, 1979. [5] Lurie, K. A.,Some Problems of Optimal Bending and Tension of Elastic Plates (in Russian), Izvestiya Akademii Nauk SSSR, Mekhanika Tverdogo Tela, Vol. 14, No. 6, 1979. [6] Raitum, U. Ë.,The Extension of Extremal Problems Connected with a Linear Elliptic Equation, Soviet Mathematics Doklady, Vol. 19, No. 6, 1978. [7] Tartar, L.,Problemes de Controle des Coefficients dans des Equations aux Derivées Partielles, Springer-Verlag, New York, New York, pp. 420-426, 1975. [8] Kozlov, S. M.,Averaging of Random Operators (in Russian), Matematicheskii Sbornik, Vol. 109, No. 2, 1979. · Zbl 0422.35003 [9] Dykhne, A. M.,Conductivity of a Two-Dimensional System (in Russian), Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 59, No. 1, 1970.
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