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Integrability of optimal mappings |
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| Authors: | A V Kolesnikov |
| Institution: | (1) M. V. Lomonosov Moscow State University, Moscow |
| Abstract: | In this paper, we study the integrability of optimal mappings T taking a probability measure μ to another measure g · μ. We assume that T minimizes the cost function c and μ 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|α). |
| Keywords: | optimal mapping infimum-convolution inequality logarithmic Sobolev inequality transportation inequality Monge-Kantorovich variational problem |
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