A Duality Principle and Concerning Convex Dual Formulation for a Model in Micro-Magnetism

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. It is worth highlighting the dual functional obtained is concave in its concerning main variables, which correspond to the Lagrange multipliers for the respective related constraints. Finally, 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.