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 opt...
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| Format: | eBook |
| Language: | English |
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Cambridge ; New York, NY
Cambridge University Press
2023
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| Series: | Cambridge studies in advanced mathematics
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| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of 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