Field theories in the modern calculus of variations

Abstract

Two methods of construction of fields of extremals ("geodesic coverings") in the generalized problem of Bolza are given and, as a consequence, sufficient conditions for optimality in a form similar to Weierstrass’ are formulated. The first field theory is an extension of Young’s field theory— "concourse of flights" for our problem; the other describes a nonclassical treatment of field theory which allows one to reject the "self-multiplier restriction".