We characterize generalized Young measures, the so-called DiPerna–Majda measures which
are generated by sequences of gradients. In particular, we precisely describe these
measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech.
Anal. 86 (1984) 251–277]. As a consequence we get new results on
weak W1,2(Ω; ℝ3) sequential
continuity of
u → a· [Cof∇u] ϱ,
where Ω ⊂ ℝ3 has a smooth boundary and a,ϱ
are certain smooth mappings.