On infinite-dimensional variational problems
Анотація
We consider an extremal problem for the functional where X is a Banach spase, μ is a smooth measure on X, Ais a.map from a functional space B 1(X) to a functional space B 2(X), and extend the main results of classical calculus of variations to the case under consideration. The infinite-dimensional analogs of the Euler-Lagrange equation, the Noether theorem, the canonical Hamilton system are obtained. The illustrations of these results for (where z(x) is a vector field) are given. The example related to the stochastic optimal control theory is considered
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