Abstract

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear model in elasticity. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. In a subsequent section, we present a global existence result for such a concerning model in elasticity. Finally, in the last sections, we develop duality principles and relaxation procedures for a related model in phase transition.