Geodesic
On distributional adjugate and derivative of the inverse
Stanislav Hencl1 ; Aapo Kauranen2 ; Jan Malý1
1 Charles University, Department of Mathematical Analysis
2 Universitat Autònoma de Barcelona, Departament de Matemàtiques
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 21-42.

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Let $\Omega\subset\mathbf{R}^3$ be a domain and let $f\colon\Omega\to\mathbf{R}^3$ be a bi-$BV$ homeomorphism. Very recently in [16] it was shown that the distributional adjugate of $Df$ (and thus also of $Df^{-1}$) is a matrix-valued measure. In the present paper we show that the components of Adj $Df$ coincide with the components of $Df^{-1}(f(U))$ as measures and that the absolutely continuous part of the distributional adjugate Adj $Df$ equals to the pointwise adjugate adj $Df(x)$ a.e. We also show the equivalence of several approaches to the definition of the distributional adjugate.  
Keywords: bounded variation, distributional Jacobian

Stanislav Hencl 1 ; Aapo Kauranen 2 ; Jan Malý 1

1 Charles University, Department of Mathematical Analysis
2 Universitat Autònoma de Barcelona, Departament de Matemàtiques 
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Stanislav Hencl; Aapo Kauranen; Jan Malý. On distributional adjugate and derivative of the inverse. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 21-42. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a1/