Homogenization of elasticity problems on singular structures

Izvestiya Mathematics

Volumn 66, Issue 2, 2002, Pages 299-365

  Zhikov, V V ^a  

^a NONE

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EID: 33748487201     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2002v066n02ABEH000380     Document Type: Article

References (23)

1. N. S. Bakhvalov and G. P. Panasenko, Homogenization: averaging processes in periodic media, Nauka, Moscow 1984; English transl., Kluwer, Dordrecht-Boston-London 1989.
2. V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, Homogenization of differential operators, Nauka, Moscow 1993;
3. English transl., Homogenization of differential operators and integral functional, Springer-Verlag, Berlin-New York 1994.
4. O. A. Oleinik, A. S. Shamaev and G. A. Yosifian, Mathematical problems in the theory of strongly inhomogeneous elastic media, Moscow State Univ. Press, Moscow 1990;
5. English transl., Mathematical problems in elasticity and homogenization, North-Holland, Amsterdam 1992.
6. A. Braides and A. Defranceschi, Homogenization of multiple integrals, Oxford Series Math. Appl., vol. 12, Clarendon Press, Oxford 1998.
7. J. Saint Jean Paulin and D. Cioranescu, Homogenization of reticulated structures, Appl. Math. Sci., vol. 136, Springer-Verlag, Berlin-New York 1999.
8. E. Sanchez-Palencia, Homogenization techniques for composite media, Springer-Verlag, Berlin-New York 1987.
9. V. V. Zhikov, "Connectedness and homogenization. Examples of fractal conductivity", Mat. Sb. 187:8 (1996), 3-40;
10. English transl., Sb. Math. 187 (1996), 1109-1147.
11. V. V. Zhikov, "On the homogenization technique for variational problems", Funktsional. Anal. i Prilozhen. 33:1 (1999), 14-29;
12. English transl., Functional Anal. Appl. 33 (1999), 11-24.
13. P. G. Ciarlet, Mathematical elasticity. II. Theory of plates, Studies in Math. and Applications, vol. 27, Elsevier, Amsterdam 1997.
14. E. Acerbi, G. Butazzo and D. Percivale, "Thin inclusion in linear elasticity: a variational approach", J. Reine Angew. Math. 386 (1988), 99-115.
15. R. V. Kohn and M. Vogelius, "A new model for thin plates with rapidly varying thickness. II. A convergence proof", Quart. Appl. Math. 43 (1985), 1-22.
16. U. Mosco, "Composite media and asymptotic Dirichlet forms", J. Fund. Anal. 123 (1994), 368-421.
17. S. A. Nazarov, "Korn's inequalities for functions of spatial bodies and thin rods", Math. Methods Appl. Sci. 20:3 (1997), 219-243.
18. G. Bouchitté, G. Buttazzo and P. Seppecher, "Energies with respect to a measure and applications to low-dimensional structures", Calc. Var. Partial Differential Equations 5:1 (1997), 37-54.
19. G. Allaire, "Homogenization and two-scale convergence", SIAM J. Math. Anal. 23 (1992), 1482-1518.
20. V. V. Zhikov, "On an extension of the method of two-scale convergence and an application", Mat. Sb. 191:7 (2000), 31-72;
21. English transl., Sb. Math. 191 (2000), 973-1015.
22. V. V. Zhikov, "Weighted Sobolev spaces", Mat. Sb. 189:8 (1998), 27-58;
23. English transl., Sb. Math. 189 (1998), 1139-1170.