On duality principles for scalar and vectorial multi-well variational problems

This work develops duality applicable to vectorial problems in the calculus of variations. The results can be used to compute solutions related to the relaxation of non-convex problems, such as vectorial phase transition models, particularly as the primal approaches have no solutions in the classical sense. In this latter case, the solution of the dual problem is a weak cluster point of minimizing sequences for the original formulation. Here we are not restricted to two or three wells only, the results developed are suitable for more general situations.