Uniqueness and Convexity in the Calculus of Variations

In the Calculus of Variations, convexity plays a seemingly irreplaceable role.

For vectorial problems, however, for good reasons a whole zoo of its generalizations was introduced. It ranges  from notions based on very classical

observation over explicite, but only partially understood,

characterizations to very practical  conditions.

Recently a new convexity concept emerged, in differnt research projects for

different reasons. We are interested in it, since it describes stabilty of

uniqueness of minimizers under a huge class of pertubations.

We'll discuss differences, and particular

agreement with other convexity notions for vectorial problems.