Remarks on the Total Variation of the Jacobian
نویسنده
چکیده
The total variation T V (u) of the Jacobian determinant of non-smooth vector fields u has recently been studied in [2]. We focus on the subclass u(x) = ϕ(x/|x|) of homogeneous extensions of smooth functions ϕ : ∂B n → R n. In the case n = 2, we explicitely compute T V (u) for some relevant examples exhibiting a gap with respect to the total variation |DetDu| of the distributional determinant. We then provide examples of functions with |DetDu| = 0 and T V (u) = +∞. We finally show that this gap phenomenon doesn't occur if n ≥ 3.
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