ABSTRACT
The basic result of the extremum theory is the necessary condition of minimum for the differentiable functions. By the stationary condition, the derivative of the function at the point of minimum is equal to zero. We can extend this result to the problem of minimization for the smooth functionals. Particularly, the G a ^ $ \hat{\mathrm{a}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152448/5968d418-c0e2-45a5-91c4-37245a5e7358/content/inline-math5_1.tif"/> teaux derivative of the functional at the point of its minimum is equal to zero. Then the necessary condition of minimum for the differentiable functional on a convex set is the variational inequality (see Chapter 1).
