2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71803We show the existence of the strong solutions of the Monge-Ampere equation for the log-concave measures without any regularity assumption. In particular the measures with density of the form $\exp -f$, where $f$ is an $H$-convex function which may take the value $\infty$ on a set of positive measure are included.24 pagesAnalysis of PDEsProbability60H07,60H05,46G12,47H05text