CONVEX FUNCTIONS OCCURRING IN VARIATIONAL PROBLEMS AND THE ABSOLUTE MINIMUM PROBLEM
Alexander Davidovich Ioffe · Mathematics of the USSR-Sbornik · 1972
For the minimum problem of the functional (where , and the case corresponds to some constraints imposed on and ) we consider the problem of the existence of a function which has the following property: if t) is a minimizing sequence, then, for any and which , and for any , (every function which has this property yields a necessary condition for the absolute minimum). We prove existence criterions for an arbitrary and continuous function .Bibliography: 9 items.