Calculus of variations in Hilbert spaces
Levon Nurbekyan · Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) · 2012
The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional variational problems in Hilbert spaces. We obtain existence of C 2 local minimizers and prove that the value function of an optimal control problem solves corresponding Hamilton-Jacobi equation in a viscosity sense.