Geodesic
Integrability of optimal mappings
Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 546-560.

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In this paper, we study the integrability of optimal mappings $T$ taking a probability measure $\mu$ to another measure $g\cdot\mu$. We assume that $T$ minimizes the cost function $c$ and $\mu$ satisfies some special inequalities related to $c$ (the infimum-convolution inequality or the logarithmic $c$-Sobolev inequality). The results obtained are applied to the analysis of measures of the form $\exp(-|x|^{\alpha})$. 
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     author = {A. V. Kolesnikov},
     title = {Integrability of optimal mappings},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_4_a7/}
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A. V. Kolesnikov. Integrability of optimal mappings. Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 546-560. http://geodesic.mathdoc.fr/item/MZM_2006_80_4_a7/

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