Exact estimates of the conductivity of a binary mixture of isotropic materials

Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Volumn 104, Issue 1-2, 1986, Pages 21-38

  Cherkaev, A V ^b  

^a IOFFE INSTITUTE   (Russian Federation)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84974267674     PISSN: 03082105     EISSN: 14737124     Source Type: Journal    
DOI: 10.1017/S0308210500019041     Document Type: Article

References (16)

1. K. A. Lurie and A. V. Cherkaev. Exact estimates of conductivity of a binary mixture of isotropic compounds. Preprint 894, A. F. Ioffe Physical-Technical Institute (Leningrad: Acad. of Sc. USSR, 1984).
2. K. A. Lurie and A. V. Cherkaev. Accurate estimates of the conductivity of mixtures formed of two materials in a given proportion (two-dimensional problem). (In Russian.) Dokl. Akad. Nauk SSSR 264 (1982), 1128–1130.
3. K. A. Lurie and A. V. Cherkaev. Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 71–87.
4. C. B. Morrey. Quasiconvexity and the lower semicontinuity of multiple integrals. Pacific J. Math. 2 (1952), 25–53.
5. J. M. Ball, J. C. Currie and P. J. Olver. Null Lagrangians, weak continuity and variational problems of arbitrary order. J. Funct. Anal. 41 (1981), 135–174.
6. R. V. Kohn and G. Strang. Optimal design and relaxation of variational problems. Comm. Pure Appl. Math. 39 (1986), 113-137; 139-182; and to appear.
7. L. Tartar. Compensated compactness and applications to partial differential equations. In Non-Linear Analysis and Mechanics (Heriot-Watt Symp. IV), ed R. J. Knops (London: Pitman, 1979).
8. K. A. Lurie, A. V. Cherkaev and A. V. Fedorov. Regularisation of optimal design problems for bars and plates. I, II. J. Optim. Theory Appl. 37 (1982), 499–543.
9. F. Murat. Control in coefficients. Encyclopedia of Systems and Control (Oxford: Pergamon, 1983).
10. L. Tartar. Estimations fines de coefficients homogénéisées. To be published in Ennio DeGiorgi Colloquium, ed. P. Krée. Research Notes in Mathematics 125, pp. 168–187 (London: Pitman, 1985).
11. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik and Kha Thieng Ngoan. Averaging and G-convergence of differential operators. Russian Math. Surveys 34 (1979), 69–147.
12. K. A. Lurie and A. V. Cherkaev. G-closure of a set of anisotropically conducting media in the two-dimensional case. J. Optim. Theory Appl. 42 (1984), 283-304; corrig. to appear in the same journal.
13. J. M. Ball. Convexity conditions and existence theorems in non-linear elasticity. Arch. Rational Mech. Anal. 63 (1977), 337–407.
14. Z. Hashin and S. Shtrikman. A variational approach to the theory of elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11 (1963), 127–140.
15. B. Dacorogna. Weak continuity and weak lower semicontinuity for non-linear functionals. Lecture Notes in Mathematics 922 (Berlin: Springer, 1982).
16. K. A. Lurie and A. V. Cherkaev. G-closure for some particular sets of admissible material characteristics for the problem of the bending of thin elastic plates. J. Optim. Theory Appl. 42 (1984), 305-316; corrig. to appear in the same journal.