Abstract

This article develops a duality principle applicable to a originally non-convex primal variational formulation. More specifically, we develop applications to a full complex Ginzburg-Landau system in superconductivity, including a magnetic field and respective magnetic potential. 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 which may be applied to a large class of similar models in the calculus of variations. Finally, in the last sections, we present a procedure for improving the convexity conditions of an originally non-convex primal formulation which is also applied to a Ginzburg-Landau type equation.