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A note on weak approximation of minors. (English) Zbl 0910.49025
Summary: Let $$A_{p,q}(\Omega)$$, where $$\Omega\subseteq \mathbb{R}^n$$ is a bounded open domain, be the set of all mappings $$u\in W^{1,p}(\Omega,\mathbb{R}^n)$$ such that $$\text{adj }Du\in L^q$$. Among other results, we prove that if $$n-1\leq p< n$$, $$1< q<n/(n- 1)$$, then the subclass of $$A_{p,q}$$ mappings, which consists of mappings with bounded $$(n-1)$$-dimensional image, is dense in the sequential weak topology of $$A_{p,q}$$. We also extend this result to other $$A_{p,q}$$ type spaces.

##### MSC:
 49Q15 Geometric measure and integration theory, integral and normal currents in optimization 28A75 Length, area, volume, other geometric measure theory 74B20 Nonlinear elasticity 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets
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