On the total variation of the Jacobian

摘要

A characterization of the total variation TV(u, Omega) of the Jacobian determinant det Du is obtained for some classes of functions u : Omega subset of R-2 --> R-2 outside the traditional regularity space W-1,W-2(Omega; R-2). In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity x(0) is an element of Omega, i.e., u is an element of W-1,W-p (Omega; R-2) boolean AND W-1,W-infinity (Omega{x(0)}; R-2) for some p > 1. (C) 2003 Elsevier Inc. All rights reserved. [References: 26]