Guido De Philippis, Alessio Figalli
Published 2013-10-23Version 1
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.
Boundary $\varepsilon$-regularity in optimal transportation
$W^{2,1}$ regularity for solutions of the Monge-Ampère equation
Existence of weak solutions to the Ericksen-Leslie model for a general class of free energies
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