Given a bounded open set Ω ⊂ R2, we study the relaxation of the nonparametric area functional in the strict topology in BV (Ω; R2), and compute it for vortex-type maps, and more
generally for maps in W1,1(Ω; S1) having a finite number of topological singularities. We also extend the analysis to some specific piecewise constant maps in BV (Ω; S1), including the symmetric triple junction map.
