Duality Principles and Numerical Procedures for a Large Class of Non-Convex Models in the Calculus of Variations

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Moreover, we develop a general duality principle for quasi-convex relaxed formulations for some models in the vectorial calculus of variations. Concerning applications of such results are presented for a non-linear model of plates and for nonlinear elasticity. Finally, in some sections we present concerning numerical examples and the respective softwares.