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Let Ap,q(Ω), where Ω ⊆ Rn is a bounded open domain, be a set of all mappings u ∈ W1,p(Ω, Rn) such that adj Du ∈ Lq. Among other results we prove that if n − 1 ≤ p < n, 1 < q < n/(n − 1), then the subclass of Ap,q mappings, which consists of mappings with bounded (n − 1)-dimensional image, is dense in the sequential weak topology of Ap,q. We also extend this result to other Ap,q type spaces.
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