The Monge-Amp\`ere equation and its link to optimal transportation
Analysis of PDEs
2013-10-24 v1
Abstract
We survey the (old and new) regularity theory for the Monge-Amp\`ere equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Amp\`ere type equations arising in that context.
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@article{arxiv.1310.6167,
title = {The Monge-Amp\`ere equation and its link to optimal transportation},
author = {Guido De Philippis and Alessio Figalli},
journal= {arXiv preprint arXiv:1310.6167},
year = {2013}
}
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