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

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.