P.L. Lions's work on the Schwarz alternating method for convex minimization problems is generalized to a certain non-smooth situation where the non-diierentiable part of the functionals is additive and independent with respect to the decomposition. Such functionals arise naturally in plasticity where the material law is a variational inequality formulated in L 2 ((). The application to plastici...

The functional type extension of Ekeland’s variational principle [7] due to Zhong [18] is logical equivalent with it.

This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some dilecate estimates of the state and adjoint processes. This result is a generalization of Zhou’s stochastic maximum principl...

The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for the scalar field that produces field equations identical to the usual Einstein field equations minimally coupled to a scalar field. In the electromagnetic an...