6533b82dfe1ef96bd1291ee3

RESEARCH PRODUCT

Sobolev estimates for optimal transport maps on Gaussian spaces

Vincent NolotShizan Fang

subject

Mathematics::Complex VariablesGaussianProbability (math.PR)Mathematics::Analysis of PDEsGaussian measureSobolev spaceStrong solutionssymbols.namesakeFOS: MathematicssymbolsApplied mathematicsEntropy (information theory)Fisher informationMathematics - ProbabilityAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2012-07-20Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2014.02.017