Optimal mass transport on Euclidean spaces / Francesco Maggi.

Format:

Book

Author/Creator:

Maggi, Francesco, 1978- author.

Series:

Cambridge studies in advanced mathematics ; 207.

Cambridge studies in advanced mathematics ; 207

Language:

English

Subjects (All):

Transport theory--Mathematical models.

Transport theory.

Mass transfer.

Generalized spaces.

Physical Description:

1 online resource (xx, 295 pages) : digital, PDF file(s).

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2023.

Summary:

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.

Contents:

An introduction to the Monge problem

Discrete transport problems

The Kantorovich problem

The Brenier theorem

First order differentiability of convex functions

The Brenier-McCann theorem

Second order differentiability of convex functions

The Monge-Ampere equation for Brenier maps

Isoperimetric and Sobolev inequalities in sharp form

Displacement convexity and equilibrium of gases

The Wasserstein distance W2 on P2(Rn)

Gradient flows and the minimizing movements scheme

The Fokker-Planck equation in the Wasserstein space

The Euler equations and isochoric projections

Action minimization, Eulerian velocities and Otto's calculus

Optimal transport maps on the real line

Disintegration

Solution to the Monge problem with linear cost

An introduction to the needle decomposition method.

Notes:

Title from publisher's bibliographic system (viewed on 03 Nov 2023).

Other Format:

Print version:

ISBN:

9781009179713 (ebook)

Access Restriction:

Restricted for use by site license.