Hypercomplex hyperbolic geometry

مرکز و کتابخانه مطالعات اسلامی به زبان های اروپایی

منو

" Hypercomplex hyperbolic geometry "
Markham, Sarah

Document Type	:	BL
Record Number	:	650776
Doc. No	:	dltt
Main Entry	:	De Philippis, Guido
Title & Author	:	Regularity of optimal transport maps and applications /\ Guido de Philippis
Series Statement	:	Tesi ;; 17
Page. NO	:	xix, 169 pages :: illustrations ;; 24 cm
ISBN	:	8876424563
	:	: 9788876424564
Bibliographies/Indexes	:	Includes bibliographical references
Contents	:	Introduction -- 1. An overview on optimal transportation -- 2. The Monge-Ampère equation -- 3. Sobolev regularity of solutions to the Monge Ampère equation -- 4. Second order stability for the Monge-Ampère equation and applications -- 5. The semigeostrophic equations -- 6. Partial regularity of optimal transport maps -- A. Properties of convex functions -- B. A proof of John Lemma
Abstract	:	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
Subject	:	Transportation problems (Programming)
Subject	:	Differential equations, Partial
Subject	:	Monge-Ampère equations
Subject	:	Operator theory
Subject	:	System theory-- Mathematics
Subject	:	Control theory
LC Classification	:	‭QA402.6‬‭P455 2013‬