Abstract

This article develops duality principles and respective convex dual formulations through a D.C. approach applicable to some originally non-convex primal variational formulations. More specifically, in a first step, we develop applications to a Ginzburg-Landau type equation. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. It is worth emphasizing we have obtained a convex dual variational formulation suitable for a large class of similar models in the calculus of variations.

Keywords: Duality principle, Ginzburg-Landau system in superconductivity, D.C. approach, Convex dual formulation, Calculus of variations