Sobolev regularity for Monge-Amp\`ere type equations
Analysis of PDEs
2012-11-13 v1
Abstract
In this note we prove that, if the cost function satisfies some necessary structural conditions and the densities are bounded away from zero and infinity, then strictly -convex potentials arising in optimal transportation belong to for some . This generalizes some recents results concerning the regularity of strictly convex Alexandrov solutions of the Monge-Amp\`ere equation with right hand side bounded away from zero and infinity.
Keywords
Cite
@article{arxiv.1211.2341,
title = {Sobolev regularity for Monge-Amp\`ere type equations},
author = {Guido De Philippis and Alessio Figalli},
journal= {arXiv preprint arXiv:1211.2341},
year = {2012}
}