Regularity of Optimal Transport Maps and Applications Zoom

Guido De Philippis

Regularity of Optimal Transport Maps and Applications

pp. xix-165

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This book concerns with the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory; in particular a self-contained proof of Brenier's theorem on existence of optimal transport maps and of Caffarelli's theorem on Hölder continuity of optimal maps are included. In the third and fourth chapters the Sobolev regularity of optimal transport maps is involved, while in Chapter 5 the above-mentioned results lead to a proof of the existence of an Eulerian solution to the semi-geostrophic equation. Chapter 6 is about partial regularity of optimal maps with respect to a generic cost function. More precisely it is shown that if the target and source measures have smooth densities then the optimal map is always smooth outside a closed set of measure zero.

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Titolo Regularity of Optimal Transport Maps and Applications
Autore Guido De Philippis
Editing/translation No
ISBN 978-88-7642-456-4
Anno di pubblicazione 2013
Oggetto No
Link acquista http://www.springer.com/birkhauser/mathematics/scuola+normale+superiore/book/978-88-7642-456-4?otherVersion=978-88-7642-458-8
Notes No

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