On a variational principle related to rank-one convexity

Abstract

By means of a certain variational principle, where rank-one convexity enters in a fundamental way as part of feasibility, we construct a whole class of rank-one convex functions. We show the existence of optimal paths and motivate our analysis by the issue of the equivalence of quasiconvexity and rank-one convexity for 2 × 2 matrices.