Calculus of variations in the context of exterior differential systems

AbstractA new approach to the study of variational problems defined through functionals given by multiple integrals is presented. This work is based on techniques from the theory of exterior differential systems. Different kinds of boundary conditions are formulate for well-posed variational problems. Sufficient conditions for an integral manifold to be a local extremum are established. Applications to the study of string theory as well as some other examples are discussed