Regularity of Optimal Transport Maps and Applications / by Guido De Philippis
(Publications of the Scuola Normale Superiore ; 17)
| データ種別 | 電子ブック |
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| 出版情報 | Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale , 2013 |
| 本文言語 | 英語 |
| 大きさ | Approx. 190 p : online resource |
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| 一般注記 | 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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| 著者標目 | *Philippis, Guido De author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Calculus of variations FREE:Mathematics FREE:Calculus of Variations and Optimal Control; Optimization |
| 分 類 | DC23:515.64 |
| 巻冊次 | ISBN:9788876424588 
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| ISBN | 9788876424588 |
| URL | http://dx.doi.org/10.1007/978-88-7642-458-8 |
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