Regularity of Optimal Transport Maps and Applications (Paperback, 2013 ed.)

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.

General

Imprint:	Scuola Normale Superiore
Country of origin:	Italy
Series:	Publications of the Scuola Normale Superiore, 17
Release date:	September 2013
First published:	2013
Authors:	Guido Philippis
Dimensions:	240 x 150 x 15mm (L x W x T)
Format:	Paperback
Pages:	190
Edition:	2013 ed.
ISBN-13:	978-88-7642-456-4
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Promotions
LSN:	88-7642-456-3
Barcode:	9788876424564

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