Inserted: 12 sep 2008
Last Updated: 17 feb 2009
Journal: Calc. Var. Par. Diff. Eq.
In november I gave a talk in Pisa about this paper and when I said "the proof by De Pascale and Pratelli has this problem only: it is LONG", most of the people understood "WRONG". I'm very sorry, it was not what I meant. You can trust Gigi and Aldo, their proof works very well !!
The paper presents some short proofs for transport density absolute continuity and $L^p$ estimates. Most of the previously existing results which were proven by geometric arguments are re-proved through a strategy based on displacement interpolation and on approximation by discrete measures; some of them are partially extended.
Keywords: Transport density, displacement interpolation