199 citations · 522 across the 42 of their papers we have counts for
4 papers · 1 filter
Partial Regularity for optimal transport maps
Guido De Philippis, Alessio Figalli
We prove that, for general cost functions on , or for the cost on a Riemannian manifold, optimal transport maps between smooth densities are always smooth out…
A global existence result for the semigeostrophic equations in three dimensional convex domains
Luigi Ambrosio, Maria Colombo, Guido De Philippis +1
Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions on the initial data we prove global-in-time existence of Eulerian distribution…
A note on interior estimates for the Monge-Ampere equation
Guido De philippis, Alessio Figalli, Ovidiu Savin
By a variant of the techniques introduced by the first two authors in [DF] to prove that second derivatives of solutions to the Monge-Ampere equation are locally in , we o…
Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps
Guido De Philippis, Alessio Figalli
The aim of this note is to show that Alexandrov solutions of the Monge-Ampere equation, with right hand side bounded away from zero and infinity, converge strongly in $W^{2,1}_{loc…