  In this paper we present explicit estimate for Lipschitz constant of solution
to a problem of calculus of variations. The approach we use is due to
Gamkrelidze and is based on the equivalence of the problem of calculus of
variations and a time-optimal control problem. The obtained estimate is used to
compute complexity bounds for a path-following method applied to a convex
problem of calculus of variations with polyhedral end-point constraints.
