A note on weak approximation of minors

Abstract

Let $A_{p,q}(\Omega )$, where $\Omega \subseteq R^n$ is a bounded open domain, be a set of all mappings $u\in W^{1,p}(\Omega ,R^n)$ such that $\mathrm{adj}Du\in L^q$. Among other results we prove that if $n-1\le p<n$, $1<q<n/(n-1)$, 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.