On the total variation of the Jacobian O

A characterization of the total variation TV(u,Ω) of the Jacobian determinant det Du is obtained for some classes of functions u:Ω⊂R2→R2 outside the traditional regularity space W1,2(Ω;R2). In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity x0∈ Ω, i.e., u∈W1,p(Ω;R2)∩W1,∞(Ω ⧹{x0};R2) for some p>1.