By Filippo Santambrogio

This monograph offers a rigorous mathematical advent to optimum shipping as a variational challenge, its use in modeling quite a few phenomena, and its connections with partial differential equations. Its major objective is to supply the reader with the options essential to comprehend the present learn in optimum shipping and the instruments that are most valuable for its applications. Full proofs are used to demonstrate mathematical techniques and every bankruptcy contains a part that discusses purposes of optimum shipping to numerous components, equivalent to economics, finance, capability video games, photo processing and fluid dynamics. Several themes are coated that experience by no means been formerly in books in this topic, resembling the Knothe delivery, the houses of functionals on measures, the Dacorogna-Moser move, the formula through minimal flows with prescribed divergence formula, the case of the supremal fee, and the main classical numerical methods. Graduate scholars and researchers in either natural and utilized arithmetic drawn to the issues and functions of optimum shipping will locate this to be a useful resource.

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