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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