9788876424564 - regularity of optimal transport maps and applications (publications of the scuola normale superiore, 17, band 17) von philippis, guido (5 Ergebnisse)
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Paperback. Zustand: Brand New. 2013 edition. 190 pages. 9.25x6.00x0.75 inches. In Stock.
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Zustand: New. 2013. 2013th Edition. paperback. . . . . . Books ship from the US and Ireland.
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Taschenbuch. Zustand: Neu. Neuware - 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 T…heorem 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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Zustand: New. 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 optimal maps and their applications too the se.
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Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | 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 o…ptimal 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.
