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Introduction to Optimal Transport Theory

Published 20 Sep 2010 in math.CA, math.AP, math.DG, and math.PR | (1009.3856v1)

Abstract: These notes constitute a sort of Crash Course in Optimal Transport Theory. The different features of the problem of Monge-Kantorovitch are treated, starting from convex duality issues. The main properties of space of probability measures endowed with the distances $W_p$ induced by optimal transport are detailed. The key tools to put in relation optimal transport and PDEs are provided.

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