Calculus of Variations and Geometric Measure Theory

G. De Philippis

Weak notions of Jacobian determinant and relaxation

created by dephilipp on 20 Feb 2010
modified on 03 Oct 2010


Accepted Paper

Inserted: 20 feb 2010
Last Updated: 3 oct 2010

Journal: ESAIM Control Optim. Calc. Var
Year: 2010

Reviewed version


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: relaxation, Total variation, Topological degree, distributional determinant