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Matematicheskie Zametki, 2006, Volume 80, Issue 4, Pages 546–560
DOI: https://doi.org/10.4213/mzm2847 (Mi mzm2847) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Integrability of optimal mappings

A. V. Kolesnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (514 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm2847
Abstract: 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 $\exp(-|x|^{\alpha})$.
Received: 10.10.2005
Revised: 03.06.2006
English version:
Mathematical Notes, 2006, Volume 80, Issue 4, Pages 518–531
DOI: https://doi.org/10.1007/s11006-006-0170-z
Bibliographic databases:
UDC: 517.988.38
Language: Russian
Citation: A. V. Kolesnikov, “Integrability of optimal mappings”, Mat. Zametki, 80:4 (2006), 546–560; Math. Notes, 80:4 (2006), 518–531
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Математические заметки Mathematical Notes
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