Titlebook: Regularity of Optimal Transport Maps and Applications; Guido Philippis Book 2013 The Editor(s) (if applicable) and The Author(s), under ex

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,The Monge-Ampère equation,a proof of Caffarelli .. regularity theorem [18, 20]. Many of the tools developed in this Chapter will play a crucial role in the proof of the Sobolev regularity in Chapter 3. In the last Section we show, without proofs, how to build smooth solutions to the Monge-Ampère equation throughout the metho

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Book 2013rove 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.

金哥占卜者

Book 2013he 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 Ch

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2239-1460 nt results like Sobolev regularity and Sobolev stability forIn 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 exis

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,Second order stability for the Monge-Ampère equation and applications,nd ? respectively. By the convexity of .. and ., and the uniqueness of solutions to (2.1), it is immediate to deduce that .. → . uniformly, and ?.. → ?. in ... (Ω) for any . < ∞. What can be said about the strong convergence of ....? Due to the highly nonlinear character of the Monge-Ampère equation, this question is nontrivial.

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