A nonintersection property for extremals of variational problems with vector-valued functions
The author considers the classical problem of calculus of variations, i.e., the one of minimizing the integral of some Lagrangian function over a function whose end-point values are fixed (the function of time to be minimized has value in an Euclidean space). He studies the class of functions of time which are bounded and solution of these problems of calculus of variations for any initial and final time, with of course compatible end-point conditions. His main results are that (i) if such a function has the same value at two different times, then it is periodic, (ii) if two such functions have the same value at given times, then they coincide (perhaps up to a translation).
scientific article; zbMATH DE number 5138727