Geodesic
Weak notions of jacobian determinant and relaxation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 1, pp. 181-207

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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.

DOI : 10.1051/cocv/2010047
Classification : 49J45, 28A75
Keywords: distributional determinant, topological degree, relaxation 
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     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/}
}
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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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