Quasiconvexity versus group invariance
  The lower invariance under a given arbitrary group of diffeomorphisms extends the notion of quasiconvexity. The non-commutativity of the group operation (the function composition) modifies the classical equivalence between lower semicontinuity and quasiconvexity.   In this context null lagrangians are particular cases of integral invariants of the group.   Developments of parts of this paper can be found in math.FA/0105097 . Further informations at http://irmi.epfl.ch/cag/buliga_necv.html . 
Marius Buliga