In this book we discuss the theory of optimal mass transport as first formulated by Gaspard Monge in 1781. We further discuss the important steps leading to the existence of solutions to the Monge’s problem. Next we formulate Brenier theorem which not only solves the Monge’s problem for quadratic cost function but also provides a link to a class of the Monge-Ampere equations. Finally we study the regularity of Brenier solution.
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