The Monge-Amp\`ere equation and its link to optimal transportation
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Publication:6245853
DOI10.1090/S0273-0979-2014-01459-4zbMATH Open1515.35005arXiv1310.6167WikidataQ56675559 ScholiaQ56675559MaRDI QIDQ6245853
Alessio Figalli, Guido De Philippis
Publication date: 23 October 2013
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.
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Monge-Ampère equations (35J96)
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