On Duality Principles for Scalar and Vectorial Multi-well Variational Problems

Abstract

The main focus of chapters 17 is the development of dual variational formulations for multi-well optimization problems in phase-transitions. The primal formulation may not have minimizers in the classical sense. In this case, the solution through the dual formulation is a weak limit of minimizing sequences for the original problem. This chapter was published in an article form by Nonlinear Analysis-Elsevier, reference [14].