The complete figure for second order multiple integral problems in the calculus of variations. (Short Communication).
The complete figure for second order multiple integral problems in the calculus of variations.
The Hamilton-Cartan formalism in the calculus of variations
We give an exposition of the calculus of variations in several variables. The introduction of a linear differential form studied by Cartan makes possible an invariant treatment of the Hamiltonian formalism. Noether’s theorem, the Hamilton-Jacobi equation and the second variation are discussed and a Poisson bracket is defined.
The second-order methods in discrete optimal control problems
The vanishing viscosity method in infinite dimensions
The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.
Transversality and Fields of Extremals of Multiple Integral Problems in the Calculus of Variations.