| 000 | 02519nam a22004695i 4500 | ||
|---|---|---|---|
| 001 | 978-88-7642-458-8 | ||
| 003 | DE-He213 | ||
| 005 | 20140220082931.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 130727s2013 it | s |||| 0|eng d | ||
| 020 |
_a9788876424588 _9978-88-7642-458-8 |
||
| 024 | 7 |
_a10.1007/978-88-7642-458-8 _2doi |
|
| 050 | 4 | _aQA315-316 | |
| 050 | 4 | _aQA402.3 | |
| 050 | 4 | _aQA402.5-QA402.6 | |
| 072 | 7 |
_aPBKQ _2bicssc |
|
| 072 | 7 |
_aPBU _2bicssc |
|
| 072 | 7 |
_aMAT005000 _2bisacsh |
|
| 072 | 7 |
_aMAT029020 _2bisacsh |
|
| 082 | 0 | 4 |
_a515.64 _223 |
| 100 | 1 |
_aPhilippis, Guido. _eauthor. |
|
| 245 | 1 | 0 |
_aRegularity of Optimal Transport Maps and Applications _h[electronic resource] / _cby Guido Philippis. |
| 264 | 1 |
_aPisa : _bScuola Normale Superiore : _bImprint: Edizioni della Normale, _c2013. |
|
| 300 |
_aApprox. 190 p. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
||
| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
||
| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 |
_aPublications of the Scuola Normale Superiore ; _v17 |
|
| 520 | _aIn 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. | ||
| 650 | 0 | _aMathematics. | |
| 650 | 0 | _aMathematical optimization. | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aCalculus of Variations and Optimal Control; Optimization. |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9788876424564 |
| 830 | 0 |
_aPublications of the Scuola Normale Superiore ; _v17 |
|
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-88-7642-458-8 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c99300 _d99300 |
||