Optimal Transport for Applied Mathematicians Calculus of Variations, PDEs, and Modeling /

• Main Author: Santambrogio, Filippo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Edition: 1st ed. 2015.
• Series: Progress in Nonlinear Differential Equations and Their Applications, 87
• Subjects: Mathematics.; Measure theory.; Differential equations.; Partial differential equations.; Calculus of variations.; Calculus of Variations and Optimal Control; Optimization.; Ordinary Differential Equations.; Partial Differential Equations.; Measure and Integration.

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current r...

Table of Contents:

• Preface
• Primal and Dual Problems
• One-Dimensional Issues
• L^1 and L^infinity Theory.- Minimal Flows.- Wasserstein Spaces
• Numerical Methods
• Functionals over Probabilities.- Gradient Flows
• Exercises
• References
• Index.    .