We characterize generalized Young measures, the so-called DiPerna–Majda measures whichare generated by sequences of gradients. In particular, we precisely describe thesemeasures 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 onweak W1,2(Ω; ℝ3) sequentialcontinuity ofu → a· [Cof∇u] ϱ,where Ω ⊂ ℝ3 has a smooth boundary and a,ϱare certain smooth mappings.
