Weak Transportation Problem and Contraction Theorem

Student: Ahmetov Janat

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2020

In this paper weak transport problem is considered. We will introduce existence and cyclical monotonicity by analogy with classical transport problem. Also we will establish connection of weak transport problem with the wasserstein distance. Finally, we will consider weak transport problem with quadratic costs and prove the contraction theorem. Moreover, we will find new conditions under which transport map is lipchitz.

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