Abstract

This article develops a duality principle applicable to originally non-convex primal variational formulations. More specifically, we establish a convex (in fact concave) dual variational formulation for a model in micro-magnetism. 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, including models in elasticity and phase transition.