Inserted: 20 feb 2010
Last Updated: 3 oct 2010
Journal: ESAIM Control Optim. Calc. Var
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