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

V. V. Zhikov


Abstract: 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.

UDC: 519.3

MSC: Primary 49A50, 49A55, 54A20; Secondary 34C29, 34C35, 35J20, 46E30, 46E35, 52A99, 54C65, 5

Received: 23.08.1982

 English version: Mathematics of the USSR-Izvestiya, 1984, 23:2, 243–276

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