Weak notions of Jacobian determinant and relaxation
Scuola Normale Superiore, P.za dei Cavalieri 7, 56100
Received: 15 March 2010
Revised: 15 July 2010
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.
Mathematics Subject Classification: 49J45 / 28A75
Key words: Distributional determinant / topological degree / relaxation
© EDP Sciences, SMAI, 2010