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.
@article{AFM_2021_46_1_a1,
author = {Stanislav Hencl and Aapo Kauranen and Jan Mal\'y},
title = {On distributional adjugate and derivative of the inverse},
journal = {Annales Fennici Mathematici},
pages = {21--42},
year = {2021},
volume = {46},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a1/}
}
TY - JOUR
AU - Stanislav Hencl
AU - Aapo Kauranen
AU - Jan Malý
TI - On distributional adjugate and derivative of the inverse
JO - Annales Fennici Mathematici
PY - 2021
SP - 21
EP - 42
VL - 46
IS - 1
UR - http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a1/
LA - en
ID - AFM_2021_46_1_a1
ER -
%0 Journal Article
%A Stanislav Hencl
%A Aapo Kauranen
%A Jan Malý
%T On distributional adjugate and derivative of the inverse
%J Annales Fennici Mathematici
%D 2021
%P 21-42
%V 46
%N 1
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a1/
%G en
%F AFM_2021_46_1_a1
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/
