5 citations · 10 across the 3 of their papers we have counts for
3 papers
math.AP2008★ 5 cited
On flows associated to Sobolev vector fields in Wiener spaces: an approach à la DiPerna-Lions
Luigi Ambrosio, Alessio Figalli
In this paper we extend the DiPerna-Lions theory on ODEs with Sobolev vector fields to the setting of abstract Wiener spaces.
math.OC2007★ 5 cited
Optimal transportation on non-compact manifolds
Albert Fathi, Alessio Figalli
In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compa…
math.DS2007
On the Hausdorff Dimension of the Mather Quotient
Albert Fathi, Alessio Figalli, Ludovic Rifford
Under appropriate assumptions on the dimension of the ambient manifold and the regularity of the Hamiltonian, we show that the Mather quotient is small in term of Hausdorff dimensi…