Minimizing Sequences

Abstract

In this section we consider again problems of the type

$$ \mathop{{Inf}}\limits_{{v \in C}} \int_{\Omega } {\Psi \left( {x,v(x),\nabla v(x)} \right)dx} $$

but we drop the convexity assumption. This will force our problems to have no minimizer. Then it is very natural to turn to the study of the minimizing sequences to see in particular if they present common features that could describe properties of the underlying physical problem. A tool for constructing minimizing sequences is the notion of Young measure that we will briefly explain.