| 书目名称 | Regularity of Optimal Transport Maps and Applications |
| 编辑 | Guido Philippis |
| 视频video | |
| 概述 | Essentially self-contained account of the known regularity theory of optimal maps in the case of quadratic cost.Presents proofs of some recent results like Sobolev regularity and Sobolev stability for |
| 丛书名称 | Publications of the Scuola Normale Superiore |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Book 2013 |
| 关键词 | Monge-Ampère equation; Sobolev regularity, Sobolev stability for optimal maps; general cost function; o |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-88-7642-458-8 |
| isbn_softcover | 978-88-7642-456-4 |
| isbn_ebook | 978-88-7642-458-8Series ISSN 2239-1460 Series E-ISSN 2532-1668 |
| issn_series | 2239-1460 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 18:57:58
