عنوان

Regularity of optimal transport maps and applications /

شابک

8876424563

شابک

9788876424564

شماره

dltt

عنوان اصلي

Regularity of optimal transport maps and applications /

نام عام مواد

[Book]

نام نخستين پديدآور

Guido de Philippis

نام خاص و کميت اثر

xix, 169 pages :

ساير جزييات

illustrations ;

ابعاد

24 cm

عنوان فروست

Tesi ;

مشخصه جلد

17

متن يادداشت

Includes bibliographical references

متن يادداشت

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

بدون عنوان

0

متن يادداشت

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

موضوع مستند نشده

Control theory

موضوع مستند نشده

Differential equations, Partial

موضوع مستند نشده

Monge-Ampère equations

موضوع مستند نشده

Operator theory

موضوع مستند نشده

System theory-- Mathematics

موضوع مستند نشده

Transportation problems (Programming)

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

De Philippis, Guido

تاريخ عمليات

20150828151129.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y