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Weak notions of Jacobian determinant and relaxation

Published online by Cambridge University Press:  02 December 2010

Guido De Philippis
Guido De Philippis*
Affiliation:
Scuola Normale Superiore, P.za dei Cavalieri 7, 56100 Pisa, Italy. guido.dephilippis@sns.it
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Abstract

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.

Keywords

Distributional determinanttopological degreerelaxation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 1 , January 2012 , pp. 181 - 207
Copyright
© EDP Sciences, SMAI, 2010

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