A characterization of graphs which can be approximated in area by smooth graphs

For vector valued maps, convergence in W 1,1 and of all minors of the Jacobian matrix in L 1 is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension n≥ 3 can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to a.e. 2-dimensional plane intersecting the domain.