Preface

Optimal mass transportation can be traced back to Gaspard Monge's paper in 1781. There, for engineering/military reasons, he was studying how to minimize the cost of transporting a given distribution of mass from one location to another, giving rise to a challenging mathematical problem. This problem, an optimization problem in a certain class of maps, had to wait for almost two centuries before seeing significant progress (starting with Leonid Kantorovich in 1942), even on the very fundamental question of the existence of an optimal map. Due to these connections with several other areas of pure and applied mathematics, optimal transportation has received much renewed attention in the last twenty years. Indeed, it has become an increasingly common and powerful tool at the interface between partial differential equations, fluid mechanics, geometry, probability theory, and functional analysis. At the same time, it has led to significant developments in applied mathematics, with applications ranging from economics, biology, meteorology, design, to image processing. Because of the success and impact that this subject is still receiving, we decided to create a special issue collecting selected papers from leading experts in the area.

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