Optimal Mass Transport on Euclidean Spaces

Optimal mass transport has become an active field with connections to calculus of variations, PDEs, and geometric analysis. This book provides a graduate-level introduction to the topic, focusing on optimal mass transport problems in a Euclidean setting with minimal prerequisites. It explores the relation between the Monge and Kantorovich transport problems and solves the former for both linear and quadratic transport costs.

Format: Hardback
Length: 345 pages
Publication date: 16 November 2023
Publisher: Cambridge University Press

Optimal mass transport has emerged as a vibrant and interdisciplinary field in the past three decades, with profound connections to calculus of variations, partial differential equations (PDEs), and geometric analysis. This comprehensive graduate-level introduction delves into the theoretical foundations and key concepts of optimal mass transport, making it accessible to students with a solid background in mathematics. By focusing on optimal mass transport problems in a Euclidean setting, the book introduces concepts gradually and intuitively, with minimal prerequisites. At the same time, it remains technically rigorous and conceptually comprehensive, providing a solid foundation in the subject.

Working within a familiar context, the book facilitates the rapid development of geometric intuition and establishes a strong foundation for further exploration. It explores the relationship between the Monge and Kantorovich transport problems, presenting solutions for both linear and quadratic transport costs, starting from the solution of the latter for arbitrary transport costs.

By delving into the complexities of optimal mass transport, this book offers valuable insights into a wide range of applications, including geometric modeling, fluid dynamics, and materials science. It serves as a valuable resource for researchers and students seeking to advance their understanding of this dynamic field.

ISBN-13: 9781009179706