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

Received April 29, 1999 / final version received July 21, 2000 Published online September 25, 2000 – c Springer-Verlag & EMS 2000 Abstract. For vector valued maps, convergence in W1 1 and of all minors of the Jacobian matrix in L1 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.