Geodesic
Questions of convergence, duality, and averaging for functionals of the calculus of variations
Izvestiya. Mathematics , Tome 23 (1984) no. 2, pp. 243-276

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The concept of $\Gamma$-convergence is studied for functionals of the calculus of variations (this concept was introduced and studied by Italian mathematicians in the school of De Giorgi), the concept of $\Gamma$-convergence is introduced and studied for dual functionals, and a duality theory is constructed connecting the $\Gamma$-limits of the original and the dual functionals. The problem of integral representation and the averaging problem are considered on the basis of this. Some unsolved problems are formulated. Bibliography: 22 titles. 
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     author = {V. V. Zhikov},
     title = {Questions of convergence, duality, and averaging for functionals of the calculus of variations},
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V. V. Zhikov. Questions of convergence, duality, and averaging for functionals of the calculus of variations. Izvestiya. Mathematics , Tome 23 (1984) no. 2, pp. 243-276. http://geodesic.mathdoc.fr/item/IM2_1984_23_2_a2/