Optimal Mass Transport on Euclidean Spaces

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 ideas 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.

Product details

• Authors: Francesco Maggi, Francesco (University of Texas Maggi, Maggi Francesco
• Publisher: Cambridge University Press Academic
• Languages: English
• Product format: Hardback
• Released: 16.11.2023
• EAN: 9781009179706
• ISBN: 978-1-0-0917970-6
• No. of pages: 345
• Dimensions: 160 mm x 237 mm x 25 mm
• Series: Cambridge Studies in Advanced Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Optimization, MATHEMATICS / Optimization, MATHEMATICS / Applied, MATHEMATICS / Differential Equations / General, Differential calculus & equations, Applied mathematics, Differential calculus and equations