Sobolev regularity for Monge-Ampère type equations
De Philippis, Guido · Figalli, Alessio
Original · EN
In this note we prove that, if the cost function satisfies some necessary structural conditions and the densities are bounded away from zero and infinity, then strictly c-convex potentials arising in optimal transportation belong to W²,¹⁺κ loc for some κ>0. This generalizes some recents results concerning the regularity of strictly convex Alexandrov solutions of the Monge-Ampère equation with right hand side bounded away from zero and infinity.
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