Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 271, Issue -, Pages 1007-1022Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2020.09.032
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Funding
- SNF [182565]
- NSF [DMS-1638352]
- Project MESA of the French National Research Agency (ANR) [ANR-18-CE40-006]
- Project EFI of the French National Research Agency (ANR) [ANR-17-CE40-0030]
- [ANR-11-LABX-0040-CIMI]
- [ANR-11-IDEX-0002-02]
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The article focuses on strictly log-concave measures and Gaussian distributions, discussing the optimal transport map between them and proving some properties of this mapping.
We consider strictly log-concave measures, whose bounds degenerate at infinity. We prove that the optimal transport map from the Gaussian onto such a measure is locally Lipschitz, and that the eigenvalues of its Jacobian have controlled growth at infinity. (C) 2020 Elsevier Inc. All rights reserved.
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