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240201 ||| eng |
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|a 9781009179713
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| 050 |
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4 |
|a QC175.2
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| 100 |
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|a Maggi, Francesco
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| 245 |
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|a Optimal mass transport on Euclidean spaces
|c Francesco Maggi
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| 260 |
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|a Cambridge ; New York, NY
|b Cambridge University Press
|c 2023
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| 300 |
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|a xx, 295 pages
|b digital
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| 505 |
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|a 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
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| 653 |
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|a Transport theory / Mathematical models
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| 653 |
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|a Mass transfer
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| 653 |
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|a Generalized spaces
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 490 |
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|a Cambridge studies in advanced mathematics
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| 856 |
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|u https://doi.org/10.1017/9781009179713
|x Verlag
|3 Volltext
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| 082 |
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|a 530.138
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| 520 |
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|a 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
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