Direct approach to the problem of strong local minima in calculus of variations

The paper introduces a general strategy for identifying strong local minimizers of variational functionals. It is based on the idea that any variation of the integral functional can be evaluated directly in terms of the appropriate parameterized measures. We demonstrate our approach on a problem of W-1,W-infinity sequential weak-* local minima - a slight weakening of the classical notion of strong local minima. We obtain the first quasiconvexity-based set of sufficient conditions for W-1,W-infinity sequential weak-* local minima.