Regularity of the Monge-Ampère equation in Besov's space

Alexander V. Kolesnikov, Sergey Yu. Tikhonov

Let $\mu =e^{-V}dx$ be a probability measure and $T=\nabla \Phi$ be the optimal transportation mapping pushing forward $\mu$ onto a log-concave compactly supported measure $ν= e^{-W}…