Rank one property for derivatives of functions with bounded variation. (English) Zbl 0791.26008

The basic result of this well organized and clearly written paper is contained in the following Theorem: Let \(\Omega\) be an open subset of \(\mathbb{R}^ n\), let \(u\) be a function of bounded variation of \(\Omega\) into \(\mathbb{R}^ m\) and denote by \(D_ s u\) the part of \(Du\) which is singular with respect to Lebesgue measure. Then \(D_ s u\) is a rank one measure and this means that for \(| D_ s u|\) almost all \(x\) the matrix \([dD_ s u/d| D_ s u|](x)\) has rank one.


26B30 Absolutely continuous real functions of several variables, functions of bounded variation
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