Regularity of Optimal Transport Maps and Applications

Language: English

Published by Scuola Normale Superiore Sep 2013, 2013

8876424563 / 9788876424564

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Neuware - In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier' theorem on existence of optimal transport maps and of Caffarelli's Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero.

Seller Inventory # 9788876424564

Title
Regularity of Optimal Transport Maps and Applications
Author
Guido Philippis
Publisher
Scuola Normale Superiore Sep 2013
Publication year
2013
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
8876424563
ISBN 13
9788876424564
Item weight
392 grams
Dimensions
241x154x17 mm

AHA-BUCH GmbH

Einbeck, Germany

5-star seller

AbeBooks seller since August 14, 2006

Shipping rates from Germany to U.S.A.

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