New proof for the regularity of Monge–Ampère type equations

Global regularity of optimal mappings in non-convex domains

“…The interior regularity was developed by many people, see for example [3,4,16,22,31], the books [19,20,21] and references therein. Very recently, a new proof was found in [35], using the Green function of the linearised Monge-Ampère equation.…”