On the total variation of the Jacobian

Abstract

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. © 2003 Elsevier Inc. All rights reserved.