Questions of convergence, duality, and averaging for functionals of the calculus of variations

V. V. Zhikov

Izvestiya. Mathematics , Tome 23 (1984) no. 2, pp. 243-276.

Résumé

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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