Distributional Jacobian equal to $H^{1}$ measure

Stanislav Hencl; Zhuomin Liu; Jan Malý

doi:10.1016/j.anihpc.2013.08.002

JournalsaihpcVol. 31, No. 5pp. 947–955

Distributional Jacobian equal to $H^{1}$ measure

Stanislav Hencl
Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic
Zhuomin Liu
Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic
Jan Malý
Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic

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Abstract

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.

Cite this article

Stanislav Hencl, Zhuomin Liu, Jan Malý, Distributional Jacobian equal to $H^{1}$ measure. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 5, pp. 947–955

DOI 10.1016/J.ANIHPC.2013.08.002