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Weak notions of jacobian determinant and relaxation

Guido De Philippis — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the and the , 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.

Weak notions of Jacobian determinant and relaxation

Guido De Philippis — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the and the , 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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