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Field name	Details
Dewey Class	515.64 (DDC 23)
Title	Regularity of Optimal Transport Maps and Applications ([Ebook]) / by Guido Philippis.
Author	De Philippis, Guido
Other name(s)	SpringerLink (Online service)
Publication	Pisa : Scuola Normale Superiore
Publication	, 2013.
Physical Details	Approx. 190 pages : online resource.
Series	Publications of the Scuola Normale Superiore ; 17
ISBN	9788876424588
Summary Note	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 Brenierâ 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.:
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-88-7642-458-8
Links to Related Works	Subject References: Calculus of variations and optimal control; optimization . Mathematical optimization . Mathematics . Optimization . Authors: De Philippis, Guido . Corporate Authors: SpringerLink (Online service) . Series: Publications of the Scuola Normale Superiore . Classification: 515.64 (DDC 23) .

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Regularity of Optimal Transport Maps and Applications

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