On duality principles for non-convex optimization with applications to superconductivity and some existence results for a model in non-linear elasticity

TL;DR

This paper develops duality principles for non-convex optimization problems, applying them to superconductivity models and elasticity, providing new theoretical insights and existence results.

Contribution

It introduces duality principles for non-convex problems with applications to superconductivity and elasticity, extending existing theoretical frameworks.

Findings

Duality principles applicable to Ginzburg-Landau system.

Global existence results for a nonlinear elasticity model.

Extension of duality theory to include magnetic fields.

Abstract

This article develops duality principles applicable to the Ginzburg-Landau system in superconductivity. The main results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. In the second section, we present the general result for the case including a magnetic field and the respective magnetic potential in a local extremal context. Finally, in the last section we develop some global existence results for a model in elasticity.