Geodesic
To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 23-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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A weighted Sobolev space is constructed in which smooth functions are not dense and their closure is of codimension one. With the help of this weighted space, counterexamples are constructed to natural hypotheses on the passage to the limit in non-uniformly-elliptic equations and on the structure of the limit equation. 
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V. V. Zhikov. To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 1, pp. 23-39. http://geodesic.mathdoc.fr/item/FAA_2001_35_1_a2/

[1] Lavrentiev M., “Sur quelques problems du calcul variations”, Ann Mat. Pura Appl., 4 (1926), 7–28 | DOI | MR

[2] Zhikov V. V., “O vesovykh sobolevskikh prostranstvakh”, Matem. sb., 189:8 (1998), 27–58 | DOI | MR | Zbl

[3] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 1. Funktsionalnyi analiz, Mir, M., 1982 | MR

[4] Mosco U., “Composite media and asymptotic Dirichlet forms”, J. Funct. Anal., 123 (1994), 368–421 | DOI | MR | Zbl

[5] Attouch H., Variational convergence for functions and operators, Pitman, London, 1984 | MR | Zbl

[6] Zhikov V. V., “Voprosy skhodimosti, dvoistvennosti i usredneniya dlya odnogo klassa funktsionalov variatsionnogo ischisleniya”, Izv. AN SSSR, ser. matem., 47:5 (1983), 961–998 | MR | Zbl

[7] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Nauka, M., 1993 | MR | Zbl

[8] Jikov V. V., Kozlov S. M., Oleinik O. A., Homogenization of differential operators and integral functionals, Springer-Verlag, 1994 | MR

[9] Zhikov V. V., “O perekhode k predelu v nelineinykh variatsionnykh zadachakh”, Matem. sb., 183:8 (1992), 47–84 | MR | Zbl