Some remarks concerning quasiconvexity and strong convergence

Abstract

SynopsisWe show that the weak convergence of a sequence of functions in a Sobolev space plus the convergence of appropriately quasiconvex “energies” imply, in fact, strong convergence. This assertion makes rigorous, for example, the heuristic principle that “quasiconvexity damps out oscillations in the gradients” of minimising sequences in the calculus of variations.