English

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.

Keywords

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

R2 v1 2026-06-21T21:38:58.376Z