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In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.
@article{COCV_2012__18_1_181_0,
author = {De Philippis, Guido},
title = {Weak notions of jacobian determinant and relaxation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {181--207},
publisher = {EDP-Sciences},
volume = {18},
number = {1},
year = {2012},
doi = {10.1051/cocv/2010047},
mrnumber = {2887932},
zbl = {1242.49025},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010047/}
}
TY - JOUR AU - De Philippis, Guido TI - Weak notions of jacobian determinant and relaxation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 181 EP - 207 VL - 18 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010047/ DO - 10.1051/cocv/2010047 LA - en ID - COCV_2012__18_1_181_0 ER -
%0 Journal Article %A De Philippis, Guido %T Weak notions of jacobian determinant and relaxation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 181-207 %V 18 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010047/ %R 10.1051/cocv/2010047 %G en %F COCV_2012__18_1_181_0
De Philippis, Guido. Weak notions of jacobian determinant and relaxation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 1, pp. 181-207. doi: 10.1051/cocv/2010047
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