New methods of solving general constrained calculus of variations problems involving pdes

Abstract

The purpose of this paper is to indicate how to solve general constrained calculus of variations problems involving pdes. These methods follow from our earlier derivation of a Bliss type multiplier rule for the Problem of Bolza for pdes. Thus, we will reformulate this earlier work as a well-defined boundary value problem and show that the critical point solution for the reformulated problem gives the same necessary conditions as the Problem of Bolza where, in addition, we can now find the multipliers. In particular, these results will lead to new general, accurate, and efficient numerical methods to solve these important problems where no such methods exist at this time.