Regularity of optimal transport maps and applications PDF

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 tra

2.1 Regularity of optimal transportation, fully nonlinear partial differential equa- tions, and Riemannian geometry. The smoothness of optimal transport maps is ...

21 Feb 2013 ... 1.3 Regularity of optimal transport map: obstructions. In this section we consider a Riemannian manifold M of dimension n. Caffarelli's ... 19 Mar 2015 ... The regularity theory of optimal transport map with quadratic cost c ( x ... of X. As an application we show that optimal transport maps between ...

Get this from a library! Regularity of Optimal Transport Maps and Applications.. [Guido Philippis] -- Annotation 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 Get this from a library! Regularity of optimal transport maps and applications. [Guido De Philippis] -- This book is a self-contained account of the known regularity theory of optimal maps in the case of quadratic cost. It presents proofs of some recent results like Sobolev regularity and Sobolev

Regularity of Optimal Transport Maps and Applications von Guido Philippis und Verleger Edizioni della Normale. Sparen Sie bis zu 80% durch die Auswahl der eTextbook-Option für ISBN: 9788876424588, 887642458X. Die Druckversion dieses Lehrbuchs hat ISBN: 9788876424564, 8876424563. 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.