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distributional determinant

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Weak notions of Jacobian determinant and relaxation
Guido De Philippis
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 1 / January 2012

Published online by Cambridge University Press:

02 December 2010, pp. 181-207

Print publication:

January 2012
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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.