Weak notions of jacobian determinant and relaxation

De Philippis, Guido

ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 1, pp. 181-207.

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.

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