Distributional Jacobian equal to ${ℋ}^{1}$ measure
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, p. 947-955

Let $1⩽p<2$. We construct a Hölder continuous ${W}^{1,p}$ mapping of a square into ${ℝ}^{2}$ such that the distributional Jacobian equals to one-dimensional Hausdorff measure on a line segment.

@article{AIHPC_2014__31_5_947_0,
author = {Hencl, Stanislav and Liu, Zhuomin and Mal\'y, Jan},
title = {Distributional Jacobian equal to ${\mathcal{H}}^{1}$ measure},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {31},
number = {5},
year = {2014},
pages = {947-955},
doi = {10.1016/j.anihpc.2013.08.002},
zbl = {06349274},
mrnumber = {3258361},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2014__31_5_947_0}
}

Hencl, Stanislav; Liu, Zhuomin; Malý, Jan. Distributional Jacobian equal to ${\mathcal{H}}^{1}$ measure. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, pp. 947-955. doi : 10.1016/j.anihpc.2013.08.002. http://www.numdam.org/item/AIHPC_2014__31_5_947_0/

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