عنوان

Regularity of optimal transport maps and applications /

(Number (ISBN

8876424563

(Number (ISBN

9788876424564

Number

dltt

Title Proper

Regularity of optimal transport maps and applications /

General Material Designation

[Book]

First Statement of Responsibility

Guido de Philippis

Specific Material Designation and Extent of Item

xix, 169 pages :

Other Physical Details

illustrations ;

Dimensions

24 cm

Series Title

Tesi ;

Volume Designation

17

Text of Note

Includes bibliographical references

Text of Note

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

0

Text of 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 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

Control theory

Differential equations, Partial

Monge-Ampère equations

Operator theory

System theory-- Mathematics

Transportation problems (Programming)

Class number

Book number

De Philippis, Guido

Date of Transaction

20150828151129.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y