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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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