Optimal Mass Transport

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 Monges problem. Next, we formulate Brenier theorem which not only solves the Monges 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.