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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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Dalla quarta di copertina
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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Regularity of Optimal Transport Maps and Applications (Paperback)
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Birkhauser Verlag AG, Pisa, 2013
ISBN 10: 8876424563
ISBN 13: 9788876424564
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Paperback. Condizione: new. Paperback. 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 Caffarellis 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. 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 Caffarellis Theorem on Holder continuity of optimal maps. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9788876424564
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Regularity of Optimal Transport Maps and Applications: 17 (Publications of the Scuola Normale Superiore, 17)
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Condizione: New. 2013. 2013th Edition. paperback. . . . . . Codice articolo V9788876424564
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Paperback. Condizione: Brand New. 2013 edition. 190 pages. 9.25x6.00x0.75 inches. In Stock. Codice articolo x-8876424563
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Condizione: New. 2013. 2013th Edition. paperback. . . . . . Books ship from the US and Ireland. Codice articolo V9788876424564
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Regularity of Optimal Transport Maps and Applications
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Scuola Normale Superiore Sep 2013, 2013
ISBN 10: 8876424563
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Taschenbuch. Condizione: 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 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. Codice articolo 9788876424564
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Regularity of Optimal Transport Maps and Applications
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Condizione: 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. Codice articolo 103018466
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Condizione: New. pp. 190 2013th edition. Codice articolo 2697464471
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Condizione: 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 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. Codice articolo 23749727/12
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