Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 58, Issue 6, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-019-1624-y
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Funding
- University of Vienna
- Austrian Science Fund (FWF) [W1245] Funding Source: Austrian Science Fund (FWF)
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The optimal weak transport problem has recently been introduced by Gozlan et al. (J Funct Anal 273(11):3327-3405, 2017). We provide general existence and duality results for these problems on arbitrary Polish spaces, as well as a necessary and sufficient optimality criterion in the spirit of cyclical monotonicity. As an application we extend the Brenier-Strassen Theorem of Gozlan and Juillet (On a mixture of brenier and strassen theorems. , 2018) to general probability measures on Rd\under minimal assumptions. A driving idea behind our proofs is to consider the set of transport plans with a new ('adapted') topology which seems better suited for the weak transport problem and allows to carry out arguments which are close to the proofs in the classical setup.
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