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 $\exp(-|x|^{\alpha})$. 
@article{MZM_2006_80_4_a7,
     author = {A. V. Kolesnikov},
     title = {Integrability of optimal mappings},
     journal = {Matemati\v{c}eskie zametki},
     pages = {546--560},
     publisher = {mathdoc},
     volume = {80},
     number = {4},
     year = {2006},
     language = {ru},
     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/