The Monge–Ampère equation and its link to optimal transportation

De Philippis, Guido; Figalli, Alessio

doi:10.1090/S0273-0979-2014-01459-4

The Monge–Ampère equation and its link to optimal transportation
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Bull. Amer. Math. Soc. 51 (2014), 527-580 Request permission

Abstract:

We survey old and new regularity theory for the Monge–Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge–Ampère type equations arising in that context.

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