Sobolev estimates for optimal transport maps on Gaussian spaces
Probability
2012-07-23 v1
Abstract
We will study variations in Sobolev spaces of optimal transport maps with the standard Gaussian measure as the reference measure. Some dimension free inequalities will be obtained. As application, we construct solutions to Monge-Ampere equations in finite dimension, as well as on the Wiener space.
Cite
@article{arxiv.1207.4907,
title = {Sobolev estimates for optimal transport maps on Gaussian spaces},
author = {Shizan Fang and Vincent Nolot},
journal= {arXiv preprint arXiv:1207.4907},
year = {2012}
}
Comments
24 pages