Sul problema libero unidimensionale del calcolo delle variazioni

We consider the one dimentional variational problem of the calculus of variation and discuss the existence of minima among a class of absolutely continuous curves with fixed endpoints. A sufficient condition for the existence of the minimum is given; this condition is also necessary for a large class of integrands. Its development is effected by an interesting argument involving Tonelli-inspired ideas of lower-semicontinuity together with some applications of Pontrjagin's principle. A study of uniqueness is also included.