Weak notions of Jacobian determinant and relaxation

Guido De Philippis

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)181-207
Number of pages27
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number1
StatePublished - Jan 2012


  • Distributional determinant
  • Relaxation
  • Topological degree

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


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