On the total variation of the Jacobian

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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→ ℝ2outside 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.

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Fonseca, I., Fusco, N., & Marcellini, P. (2004). On the total variation of the Jacobian. Journal of Functional Analysis, 207(1), 1–32. https://doi.org/10.1016/S0022-1236(03)00111-3

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