弗朗切斯科·马吉：欧基里得空间上的至佳质量传输 Optimal Mass Transport on Euclidean Spaces

基本信息

Series:Cambridge Studies in Advanced Mathematics

Format:Hardback 345 pages, Worked examples or Exercises

Publisher:Cambridge University Press

Imprint:Cambridge University Press

ISBN:9781009179706

Published:16 Nov 2023

Weight:622g

Dimensions:160 x 236 x 28 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

优质量传递在过去三十年中已成为一个活跃的领域，与变分法、偏微分方程和几何分析有着广泛的联系。 这个研究生水平的介绍涵盖了该领域的理论基础和应用中的关键思想。 通过关注欧几里得环境中的至优公共交通问题，本书能够以渐进的、易于理解的方式以至少的先决条件介绍概念，同时保持技术和概念上的完整性。 在熟悉的环境中工作将帮助读者快速建立几何直觉，并为他们在该主题上打下坚实的基础。 本书探讨了 Monge 和 Kantorovich 传输问题之间的关系，解决前者的线性传输成本（这在几何应用中很重要）和二次传输成本（这在偏微分方程应用中很重要），从解决 后者用于任意运输成本。

Optimal mass transport has emerged in the past three decades as an active field with wide-ranging connections to the calculus of variations, PDEs, and geometric analysis. This graduate-level introduction covers the field's theoretical foundation and key points in applications. By focusing on optimal mass transport problems in a Euclidean setting, the book is able to introduce concepts in a gradual, accessible way with minimal prerequisites, while remaining technically and conceptually complete. Working in a familiar context will help readers build geometric intuition quickly and give them a strong foundation in the subject. This book explores the relation between the Monge and Kantorovich transport problems, solving the former for both the linear transport cost (which is important in geometric applications) and for the quadratic transport cost (which is central in PDE applications), starting from the solution of the latter for arbitrary transport costs.

作者简介

Francesco Maggi 是德克萨斯大学奥斯汀分校的数学教授。 他的研究兴趣包括变分法、偏微分方程和优质量传递。 他是剑桥大学出版社出版的《Sets of Finite Perimeter》和《Geometric Variational Problems》的作者。

Francesco Maggi is Professor of Mathematics at the University of Texas at Austin. His research interests include the calculus of variations, partial differential equations, and optimal mass transport. He is the author of Sets of Finite Perimeter and Geometric Variational Problems published by Cambridge University Press.