Optimal transportation with constant constraint (Q1639602)

In this paper, the authors consider optimal transportation problems with constraint, for which the upper bound \(h(x, y)\) of the density \(H\) on the product spaces is constant and \(h \geq 1\). They propose simplifications of proofs for many previous results and examples [\textit{J. Korman} et al., Calc. Var. Partial Differ. Equ. 54, No. 1, 573--584 (2015; Zbl 1331.90095); \textit{J. Korman} and \textit{R. J. McCann}, Trans. Am. Math. Soc. 367, No. 3, 1501--1521 (2015; Zbl 1305.90065)], and also present explicit examples of optimal transportation plans for all constraints \(h \geq 1\).