Regularity of Optimal Transport Maps and Applications
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 o...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Pisa :
Scuola Normale Superiore
[20..].
Cham : Springer Nature |
| Ausgabe: | 1st ed. 2013. |
| Schriftenreihe: | Theses (Scuola Normale Superiore)
17 |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Regularity of Optimal Transport Maps and Applications, Texte imprimé, 9788876424564 |
| Zusammenfassung: | 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 |
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| Beschreibung: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9788876424588 |
| ISSN: | 2532-1668 |
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